I'm also usually the "handler" for very difficult people. It's stressful and I don't like it, but I seem to be better at it than most people. I don't respond emotionally in general terms-- or at least I don't actually ACT on those responses precipitously.
My DD is the same way.
And thus it is a bad idea for people to equate EQ with introversion. Often it is quite the opposite. People can be exhausting for me partially because I can't not give 100% attention and focus to someone.
Right-- and my DH, the extravert, has no trouble at all giving some percentage of his attention to others... and he has... er... squishys' self-confessed EQ.
I have trouble handling multiple inputs when human input is put on the table, because I tend to be the 100% type.
He's not a total clod (obviously) but he does struggle some because of being an extravert (and therefore dependent upon social interactions as personal fuel) but with difficulty concerning aspects of effective communication with others. He has the communication range of-- a lion. Other creatures confuse and distress him, and he doesn't respond well.
He's somewhere in negative territory when it comes to actual empathy. I mean, it's not that he's callous-- far from it. He just can't actually
identify what another person's motivations/feelings are behind their words, body language, or other behavioral expressions very well unless they are quite like himself.
It has taken him over two decades to realize that as an introvert, I am not "depressed" or "withdrawn" just because I find a couple of nights of "social time" plenty each week. I can spend a week alone and not be 'starved' for human interaction.
Of course, I'm also his major adviser when it comes to EQ problems, and have been for years. He can't always follow through with my advice very well, but I'm seldom
wrong. Which burns him up in some ways, because he's the social one of us. LOL. I'm not social. I'm just a student of those who are. Jane Goodall of the humanoids.