Music? Science? Well, I'd have put it in 'Body & Soul' but I can't see that it matters anyway.
You're quite prepared to mention your problem to strangers here on AB, so why don't you simply go to your GP and explain your problem? I suggest that you shouldn't go seeking any specific remedy, such as beta-blockers. (Doctors tend to get p!ssed off with people who turn up demanding specific drugs, rather than trusting to their expertise). Just explain your problem and ask if the doctor can help. (I'd guess that he'd prescribe Diazepam, aka Valium, or one of its successor drugs, rather than beta-blockers, but you should be guided by his/her knowledge and experience).
Chris
PS:
I've entered, and won, public speaking competitions. I've also been interviewed on national radio and presented programmes on local radio. For me, the key to overcoming nerves was simply to tell myself that I was going to enjoy myself. If I remembered that others might be assessing my performance I would simply have frozen. So I just thought "Let's have fun!" (If you don't really enjoy playing music, why the hell are you doing it anyway? Have fun!)