Monica, I know how you feel...the only way to get over this fear of playing on stage is to do it as often as you can.
I totally bombed a performance a couple of weeks ago - I was accompanying a voice student in her departmental recital class, which meant that all 100 or so voice majors and the voice faculty were there, and she was doing a Brahms song that I was not really prepared to play, and I bombed it. It was horrible - she fired me and got a new accompanist. And I think there are two reasons why I bombed her song - 1. I didn't pick the piece, didn't really like it, and therefore couldn't make myself practice it enough, and 2. I get even more nervous playing for other people than I do just playing solo stuff, because I know if I mess up, it reflects on them just as much as on me. I wasn't prepared to play it, but I could have faked it well enough if I hadn't gotten so nervous.
But I've been playing solo stuff in my own departmental recital class (for only about 15 piano majors, most of which are music education majors rather than performance) all semester, and as the semester went on, the nerves got better and better. I can understand not wanting to play in front of people, but the more you do it, the easier it gets, I think. It's also nice if you're positioned in such a way that you can pretend that the audience isn't there!
Anyway, I bet everyone in the voice department would be flabbergasted if I told them I just passed my audition to major in piano performance.
They probably think I'm the most horrible pianist in the world...
There was another accompanist at the voice thing that I saw afterwards, and she told me to just let it roll off my shoulders. She said, "We've all been there before, more than once." And I suppose that's true. Have faith in yourself!