You are not alone. I deal with pretty much everything you describe. Once I get to a match it's like a weight being lifted off me for a few hours. If it's a very competitive match I do get a bit anxious before my first stage, but after the make ready it all disappears and I can just be me.
Even if I get moved to a squad where I don't know anyone I can quickly adapt and hold a conversation. Finding this sport when I did was literally life saving for me.
That doesn't mean I don't ever have a bad match or a squad I don't like. I still need a nap as soon as I get home and showered too, but even those days are still worth it.
I have noticed that I am more capable in the Mon-Friday world than I use to be,but it took several years to get here. I am still very much an introvert and all the baggage that comes with that, but I don't feel as much of an outcast as I use too.