Yes, the simplest criticism can make me cry, and I really take it to heart, for days, weeks, even months afterward.
It depends on the situation, though. If someone is blatantly trying to pick a fight with me, I can pick a fight back and feel damn good about it, because my adrenaline is up. But if the insult is subtle, back-handed, accidental, or the person pretends they didn't mean it/acts like it was a joke, I feel like absolute crap and often end up crying, in part because I feel powerless because I can't confront them. On the other hand, people can say some pretty harsh things to me, but if the feedback is useful, I actually get less offended than most people. For instance, if someone said to me, "Your shirt is hideous, you should change it", I might or not agree or change it, but I would think, At least I have a sense of what someone thinks of this shirt. Also, if I ask someone a question, I always appreciate an honest answer.