I can relate to you in a certain way. I am hypersensitive to people's comments and teasing whether it be negative or positive.
I take way too many things personally, beat myself up about what the person said (ie: you're so stupid, what's wrong with you, you should've known better, etc). After I'm done beating myself about it for a few minutes, it often turns to anger and resentment towards the person. It's a horrible cycle that eats away at many things such as self-esteem, relationships with others, self-worth and self-control.
A lot of it is actually overthinking. If you find yourself repeating what the person said in your head or you start analyzing, simply tell yourself to stop and that you'll think about it later. Often simply putting it off really helps and when you get around to it later, you find you really don't care anymore and just move on.
I don't know if it's your case, but you might want to find a way to raise your self-esteem (this is my case). Often I look for external validation so any little hickup in the road really affects me. You have to be confident enough not to let things bother you. Just take it as is and move on to something else. Come back to it later when you can be more objective. about what was said.
That's all the advice I can give to you at the moment. I hope it helps.