Like a lot of other people, I have pretty much the same thing. I don't like many multiplayer games, but I do occasionally play some rounds of the few I like. I break out into nervous sweats every time, lol. To a degree where it's real gross, tbh. Over the years I've learned to just laugh at myself (in a kind way, not a critical way!) over it. But really, I pretty much decided I am not obligated to play multiplayer and so I only do so when I am really in the mind space to want to. Even if my body seems to disagree 5 minutes in.
So really, unless you really want to play multiplayer I wouldn't force it. Games are supposed to be fun! (I think?) But, if the real problem is you want to play them, but trying flips a bad switch in your brain, that might be something to work your mental care provider with. When I was seeing a therapist, she gave me a lot of practices/techniques to help with various specific issues I was having. And helped me understand and process the underlying cause of why some situations were bad triggers for me. Or maybe even though your meds are working pretty well, maybe a different one, or an additional one would be even better. Good luck, and have fun.