I know I’m late to this, but I just want to say that I sympathize with you, OP.
I don’t think that it’s necessarily that you’re “too sensitive,” but that you seem to have a real reticence to communicate your feelings openly, and THAT is the problem.
Some people find slapstick hilarious, and some don’t.** Some people love to have relationships (romantic and friendly) where everyone rags on each other and gives each other shit in good fun, and some people don’t like that and show their affection/camaraderie in other ways. I’m in the second group, like you. I have had to tell certain friends that, basically, “I don’t dish it out, so I shouldn’t have to take it.” Otherwise, you’ve got an imbalanced situation.
It would be one thing if she told this embarrassing story about you, and you volleyed back with a similarly embarrassing story about her, and you all laughed. Or that this time it was her turn to rag on you, but no worries, you’d get your turn later. But you don’t take your turns, because that’s just not your way, and your dynamic becomes imbalanced.
There’s nothing wrong with not having the same sense of humor or style of showing affection as your partner. You just have to address it and find a way for you both to compromise. At the same time there is something wrong in stewing in the internal, “oh I can’t tell her because she’ll think this…and REALLY, I know I’m being ridiculous and I feel silly about that…but I think she should have been more aware of my feelings…but I’m not going to say anything because XYZ, round and round and round” thought-morass without communicating it, because it’s not fair to her.
Don’t do that. Just come right out and say, “look, it would mean a lot to me if you didn’t tell our friends stories in which I do something foolish. I don’t find it funny, I find it embarrassing. That’s just how it is.” Just be frank and matter of fact.
**Case in point, because it happened today: my friend was visiting and while she was here, my cat got his leg caught in his toy basket and FLIPPED OUT, flailing around trying to shake the basket off and climbing the walls in his terror. My friend watched this in hysterics and laughed about it for the rest of her time here. All I could think about, during his freakout and after, was, “My poor little guy was so scared. :(” He was fine, and I don’t think she’s insensitive for laughing, and I also don’t think I was oversensitive for not laughing. It just isn’t funny to me, like knock-knock jokes aren’t funny to me.