First, I think it's helpful to establish what hypersensitivity really is. The dictionary defines offense as "the act of displeasing someone, or causing resentment or affront to another person." When someone is offended, they often describe themselves as having been "wounded, hurt, upset, disappointed, resentful, or insulted." Many people, Christians included, walk in constant bondage to perpetual offendedness and hurt feelings. They have submitted to the Lord in many areas of their life but for whatever reason, they have withheld the area of emotions and feelings from Him, choosing instead to internalize and obsessively dwell upon their negative feelings of hurt, betrayal, being ostracized, etc. Since these feelings become a primary focus in their life, it inevitably leads to a vicious cycle in which those negative feelings begin to color all personal interactions, making them feel isolated from, and victimized by, others. They tend to overanalyze every action, word, and motivation and interpret them through the lens of suspicion and distrust. Soon, everything anyone says or does to them is suspect as a deliberate or subversive attack. Such individuals lose the joy they are called to have as Christian believers (John 15:11, Galatians 5:22, Philippians 4:4-8), instead focusing on the petty, inconsequential negatives, living in dejected defeat instead of as victorious and redeemed children of God. If we are willing to identify the root cause of offendedness, confess it, and willingly turn it over to God, we can reverse this downward spiral in our lives and possibly even help others to address it in their lives by our example and testimony.
Ironically, causing offense and taking offence has the same root cause — self-centeredness. This is easy to see in people who routinely cause offense. Their behavior is generally perceived to be rude, abrasive, and inconsiderate with the ulterior motive of elevating or furthering themselves in some way by putting others down. But it is equally true in those with perpetual hurt feelings who tend to be hypersensitive and self-pitying that their priority is themselves. A propensity to be personally offended almost always has at its heart, self-centeredness; hence, familiar self-pitying, self-centric statements like: "she was mean to me...I was overlooked...did you see how she looked at me?...I'm not appreciated...I never get the recognition I deserve...nobody likes me...no one cares about me...etc...etc."
Since self-centeredness is the root cause of all offense — both giving and taking offense — the solution is identical for both offense-causers and offense-takers. The Bible tells us we must die to self so that we can live to Christ (Galatians 2:20). Putting the self to death is key to letting go of hypersensitivity, touchiness, and being easily offended. We follow Christ by daily taking up our cross (Luke 9:23), willingly relinquishing our selfish "rights" and "claims," and committing our way to Him. The old nature, the self, is the tool Satan accesses to manipulate and oppress us through sin (Ephesians 2:2-3). Although it is impossible to control what others say and do to you (thereby creating an artificial environment where your feelings never get hurt), as a Christian, it is possible to control your capacity to allow your feelings to be hurt by deliberately and daily putting to death the old self nature that offense so readily feeds on.
From my own personal experience, I can tell you that most of the time I have gotten my feelings hurt it came as a direct result of becoming disillusioned with some other person, usually someone I trusted and was close to, and was therefore deeply disappointed when they let me down in some unexpected way. It is useful to remind ourselves that putting high expectations on other people who are just as fallible as we are will only ever end in disappointment. Because all mankind is born with a sin nature (Romans 3:23), every person alive will eventually fall short of our expectations and let us down. The Bible teaches that our hope and expectation should be in the Lord, not in other sinners like us. Psalm 62:5-6 says, "For God alone, O my soul, wait in silence, for my hope is from Him. He alone is my rock and my salvation, my fortress; I shall not be shaken." Putting our hope in God realigns our priorities and refocuses our attention off ourselves, our feelings, our tendencies to obsess and over-analyze, as well as off others and their outrageous treatment of us, and back onto the One — the only One — who is worthy of our hope, expectation, and trust. In other words, the cure for being easily hurt and offended by others is to draw closer to Christ.
I would encourage you that you are by no means alone with this problem. I would hazard to guess that all people, even Christians, struggle with harboring grudges and trying to get to a place where they can forgive and get past feelings of resentment towards others. I certainly have and do. But I have also found that when I am resting in Christ, trusting in Him, meditating on Him and His Word, I have peace with others — a peace that is not dependent on what they do or don't do to me, or say or don't say to me, but is instead a natural outworking or byproduct of my relationship with God. It is no accident that when Jesus identified the greatest commandment, He started with a loving relationship with the Lord; and only then, successive to that, came a loving relationship with other human beings (Matthew 22:36-40). The second originates in, depends upon, and flows out of the first.
It is important to remember that when the Bible calls us to love our neighbor, it is primarily concerned with our actions towards others, not our feelings. That is why we come across revolutionary love teachings like we find in Romans 12:20-21 which tells us to do good even to our worst enemies (who we do not feel at all like being generous, friendly, or kind towards), because we are not to be influenced by evil but to overpower it with doing good. Too often, our emphasis is on how you feel towards others while our actions and behavior are completely reactionary and secondary to our feelings (ie, because our feelings have been hurt, we become withdrawn). Instead, our actions (determination to love others in spite of how we may feel about them or think they feel about us) should principally overrule our feelings in any case. We cannot always control how we feel about someone, but we can always control how we act towards that person no matter how we feel. Since we cannot actively love when we are deliberately withdrawn, we must relinquish our "right" to withdraw, which is another way of saying what we already said — we must put to death the stubborn, offended self, surrender it to Jesus, and trust that God will grant us the good feelings that are only manufactured from obedience to Him and doing what is right. In his book Mere Christianity, CS Lewis writes this: "Nobody can always have devout feelings: and even if we could, feelings are not what God principally cares about. Christian love, either towards God or towards man, is an affair of the will."
I am a runner and I have observed that when I return to the track after having been away for an extended period of time, I have to contend with blisters that inevitably form on the backs of my heels. In a very short time away from running, the skin on my feet will soften to the point where it has become unused to the repetitive friction against my sneakers that goes hand-in-hand with running several miles. If I make a conscious decision to overlook the blisters by making a daily habit of running in spite of them, they soon harden and develop into calluses, but if I allow them to dictate my running schedule, they will prevent me from going at all. Oftentimes, spiritual truth and natural truth mimic each other. When we are aware that we tend towards hypersensitivity, we can make a similarly conscious decision to make a determined habit of overlooking the personal-offense blisters that will inevitably arise from the friction of close personal relationships. Proverbs 19:11 says, "Good sense makes one slow to anger, and it is his glory to overlook an offense." To endure in the sport of running requires that I overlook the blisters that initially form; this is a physical self-denial. To endure in the Christian walk requires that we overlook personal offenses; this is a spiritual self-denial. If we push through the initial discomfort by denying self, both physical and interpersonal blisters will inevitably develop into thicker skin.
Lastly, to keep from getting bogged down in self-pity with the very inconsequential, albeit very irritating, minutiae of life, I find it very helpful to step back and take in a broader perspective. It's what I like to call a "God's-eye-view" of things. A good place to start is Jesus Christ's life and ministry that took Him to the Cross by way of a number of humiliations, insults, afflictions, and offenses that He endured on my behalf. Then I make a mental review of the sufferings and trials undergone by the martyrs in the early church who "did not love their lives so much as to shrink from death" (Revelation 12:11). Then I remind myself of my brothers and sisters around the world, many of whom face daily persecution, hardship, torture, and death for the sake of Jesus Christ and the gospel. By the time I am done with this mental review, my afflictions, however great they initially seemed to be, never appear like anything much at all. In light of this wider perspective, I find that the burden I am made to carry is very light indeed. Additionally, when we do this, we find our focus shifting from temporary concerns to eternal matters. Paul puts it this way: "For our light momentary affliction is preparing for us an eternal weight of glory beyond all comparison. So we fix our eyes not on what is seen, but on what is unseen, since what is seen is temporary, but what is unseen is eternal" (2 Corinthians 4:17-18).
When you offend someone, you are required to sincerely and genuinely seek their forgiveness (Luke 15:17-21, Matthew 18:21-35, Ephesians 4:31-32, Colossians 3:13), trying as best you can to keep from repeating the offense in future. Once you have done that, your part is complete. Whether they forgive you or not is not your burden or your concern. Worrying about it or allowing it to discourage you from loving them unresentfully and forgiving them unreservedly is only making you susceptible to sin in your own life. Do what is right in the sight of the Lord and then move forward in faith in a positive direction. Pray about it, then let it go, seeking to draw nearer to God while consciously and deliberately abandoning self-centered feelings as "cisterns that hold no water" (Jeremiah 2:13). When we draw near to God, magnifying Him and minimizing self, He promises to draw near to us (James 4:8) and to instill in us a sense of peace that helps us forbear with others and overlook personal offenses. As Psalm 119:165 reminds us, "Those who love Your law have great peace and nothing causes them to stumble."