Sometimes the drive outweighs the anxiety surrounding it, and you just HAVE to do it no matter what. I was the same way with dance performance as a child...throwing up back stage before the recital, brilliant performance, and then hiding behind my Grannie's skirts when people wanted to talk to me about it afterward. I learned a lot of the same tricks that Marg mentioned (e.g. how to seem like you're making eye contact without actually doing so, use of costumes and makeup to look like someone else up on stage, etc.)
I still perform sometimes, and I still find it draining every time...but the need to perform is so strong -- and the drained feeling is part of it -- you've gotten it out of your system, until it fills you up again so that you think you're going to burst with it. And then you do it again, and you're empty. And it starts all over again.
My favourite dance teacher once explained it like this: "It's okay to have butterflies in your stomach. The trick is to get them to fly in formation."
Trinity