Happens to me too sometimes. If something goes wrong in a conversation (the other party makes a "weird" facial expression, smile/smirk, or says something out of place), the conversation gets stuck in my head and I get a lot of anxiety/panic for the following few minutes, thinking I somehow screwed up.
Sometimes I will replay it in my head right away to reassure myself.
Other times it creeps up to me when in bed and keeps replaying over and over.
As for your original question, no, this doesn't happen with everything, but it's probably because I've made peace with the fact that people do and will talk about me. There's no point in obsessing about it.