i have the same problem, and i'll run away from it (quit lessons). I hate performing, prefer recording.
My teacher's advice has been to take every opportunity to practise and perform in front of others, which has been really good advice, as after a few weeks, I can now look forward to playing in front of friends and family, and do so generally without nerves and shakey fingers.
But I still go all stupid-like and nervous in front of my teacher. I feel it's really holding me back, as we don't move on until I play through quite well. I've been on Burgmuller's #1 for 4 weeks now because of nerves :-/ How can I get past this?!
Well. I had my lesson a couple of days ago and I passed La Candeur I'm now onto L'Arabesque, #2 in Burgmuller During my playing in the lesson I kept thinking, "you know this; you know this! so you're nervous, so what; don't rush! you know this!" My teacher said she felt like I was starting to make friends with the piano rather than attacking it Anyway, getting beyond, and having 2 whole new pieces to practise is a huge relief. Because I learn so much more and faster at the beginning, I can go back to measuring my progress in bounds rather than limps.