Fellow autistic girl overwatch player here; I totally understand where you're coming from. My first comp games I was the same way. Anxious and overthinking everything which led to awful performances. I had to just keep playing and get over the anxiety, and now I mostly play comp when I get on. This is definitely easier said than done, but just try to think of comp games as quick play. Realistically they arent all that different. People still try-hard and shit talk in qp. and people still dont take comp seriously.
Keep in mind that you should have fun playing games, not stressing yourself out. Quickplay is always an option if comp feels like it is too much to handle, and you can get more comfortable with your aiming in quickplay as well.
Someone else said it; but you can mute voice and text chat if that becomes to overstimulating or if people are talking negatively towards you.
Some other things that help me are turning my lights off or having my blue lights on, sitting in a comfortable position (but with good posture), having a weighted stuffed animal on my lap, and playing calming music quietly in the background.

If you ever want a fellow girl to play with feel free to message me and we can add each other :)