Well, this is definitely a first to see around PB. I'm not exactly sure if it's the right board, but, regardless, it does involve behavior, so, I'll treat it as such.
Also, fair warning, I don't personally tangle with issues of nervousness much if at all, so, my suggestions may more or less be limited.
Firstly: Breathe. Breathe four seconds in, and seven seconds out. Take the opportunity before committing to each encounter to center yourself. Every trade, every skirmish, every teamfight, all have the opportunity to go awry.
Just breathe, and prepare yourself to follow through.
Second: Always have a method to bail available. Flash, Lunge, Slice & Dice, Chronobreak, etc., you can work up your confidence in your fights by having an out ready.
Third: Commit. For some players I've seen, committing to a fight can be the hardest thing to do. I've lost matches where pivotal fights were never even had because nobody wanted to set foot near the enemy. Once you've cleared your thoughts with a good breath or two, try to just hone in on a target and attack.
It could probably start off as borderline tunnelling - and, for this reason, you might be well off practicing it with Champions like Xin Zhao, Diana, or Kled, as they're sticky, survivable Divers. I especially recommend Xin Zhao since he's got a fairly simple kit and his ult can help quite a lot in making fights more breatheable.
And, lastly, for better or for worse - Have fun playing who you play. The more you play certain Champions, the more you'll understand their kit and the easier it'll be for you to get into a flow state. So, even if you can't help but panic as a fight breaks out, just try to have fun playing who you play. You'll get there eventually.
I really hope my advice wasn't...Too awful shitty, it's difficult to really posit on something I don't myself experience, but, whatever the case, I hope some of what I said helps.