To some extent your fear is normal. I am usually more stressed when playing a tournament game than when having some important exam (which is not very rational). According to Jonathan Rowson it is the "mattering that matters", chess is important because we pretend it is important. And that feels very real.
This might be not helpful, but you could try:
- Playing bots
- Playing unrated games
- Using an official account, and an unofficial "drunk" account where the result doesn't matter (not on chess.com though).
At any rate you should talk to your doctor and find out whether chess could harm your health.
I have been playing online for a few years now, and if I compare the sites to club matches, i have found Club Matches to be better.
The atmosphere is better , but sometimes Club matches make me sweat a lot, on the other hand online chess makes me stare at my screen, which is not the best for the eyes.
So there is a big difference.