When I was younger, I was what I would call "hyper sensitive" and it was a detriment to be sure because I was too concerned with what others thought or afraid of rejection or being judged etc. As I got older I realized after trying to "fit in" that I was starting to resent others, and even life itself.
I didn't want to be angry or hurt anymore. Growing up in an abusive home, there tends to also be a cycle of "self abuse" and I had to learn to see that for what it was as well, and counteract my feelings with behavior modifications basically.
Mind and emotions should ideally work together in harmony and we humans tend to favor one or the other it seems :). There are a lot of techniques you can use to start undoing some of that programming, but it's not easy.
I used to just remind myself - why does this person's opinion matter to me so much? In the grand cosmic scheme of things is what is upsetting me right now going to matter in a week? a month? If not, make a mental decision to let it go. When you start to feel hurt again, direct your mind to more positive behaviors or focus on something else and do so mindfully. In that way, you are taking power back over your feelings. It doesn't mean you lose your feelings or empathy, but that you are able to modify them.
I became happier when I formed proper boundaries with people and accepted that all of us humans are fallible, have flaws, and that it is often those very things that make us unique and special. No person on this planet is perfect, and no one should have the power over you to make you feel anything. When that happens, be mindful and redirect your energy (it's the only thing you have control of in life).