We are all sensitive, whether like to admit it or not. If a person has no sensitivities then he is a sociopath and a danger to society.
So get up [like at AA meetings] and say it "I am [your name] and I am sensitive. My feelings are hurt when I am slighted".
The question is what we do with our sensitivity. Some people spend great deal of time feeling hurt and victimized. This is self destructive. Others use their sensitivities to make sure that they don't hurt others and also trying to sooth the pain of those who have been hurt. That is holy.
So my suggestion - If you were hurt, acknowledge your pain ... and then move on. Don't wallow in it. The world is FILLED with people whose first priority is NOT that you should be happy.
Your parents hurt you? Your spouse? Friends betrayed you? Move on. Accept other people's fallibility. If you can talk it out with them then great. However, many people are impossible to talk to because they become defensive and are not self aware enough to realize where they are "holding" emotionally vis-a-vis themselves and the rest of society. Let them be. Maybe one day they will go to therapy and work through their issues. Or maybe they won't. But your task in this world is not to fix them. I suspect that you have enough to fix in yourself that will keep you busy for the duration of your stay on earth.