The word "empathy" gets misused much too often. Some people like to insist that people like me, who are on the autism spectrum, have no empathy. Not so; we simply can't read nonverbal communication, so we don't catch the nonverbal cues that tell most people what emotion they're expected to display.

In the same way, telempathy isn't the same thing as emotional empathy. It's a form of psychism that means that you mirror in your own body what other people feel in theirs. A lot of people with it end up feeling other people's illnesses and injuries, as OP does. Others pick up on the emotional states of others -- but the downside is that they get the real emotions, not the socially approved mask. Here's somebody whose father just died. The socially approved emotion she projects is grief, but maybe Daddy was a world-class jerk and she's relieved that he's gone. The telempath picks up on the relief, responds accordingly, and gets told that he's an insensitive jerk. Not so; he's too sensitive, in fact, and to the wrong thing.