Having had a lot of “fun” going off medication that was hard to take and hard to cut, I don’t know that I recommend medicine as a first line of defense. Universities usually have counselling available for free for students, and I found it very useful. Just be sure that the counselor cannot prescribe, or the tendency is too much to resist. My counselor was a Social Work graduate, and really adept at getting me to argue with myself. It was frustrating and incredibly helpful at the same time :). You might even have access to CBT.
I do understand exactly what you are talking about, although as a strong introvert I never felt the need to formally treat it (had other fish to fry also). What helped me a lot was to realize that I’m way too good at reading emotions and micro-expressions on people’s faces, and as a result I’m often likely to react emotionally to something that was either not related to me in any way (somebody’s distraction about a personal problem would be perceived as reluctance to engage with me, for example), or to something that was transient and not an illustration of the person’s final conclusion (for example, eye roll was directed at my messy notes, or at my undiplomatic phrasing, but was not contempt of me as a person). Now if I get this insignificant feeling, I try to concentrate on what the person is saying verbally and act according to that. Then I go regroup and ideally do something that I feel capable of, and try again the next day. Usually if there is really a problem it will become clear over multiple consecutive interactions, in which case I regroup and go talk to somebody else (which is easier said than done, but age fortunately does help here).