Hi Clueless One,
I used to feel exactly like you. The thought of playing in front of anybody (even my teacher!!) terrified me and just like you my hands were shaking and when I managed to play I sounded like a robot playing! There's been a lot of threads on this forum about nerves and some comments really helped me.
I don't get nervous at all in lessons anymore. I always go with the attitude that I am a learner, my teacher is there to help. She knows how long I've been learning for and is not expecting me to play perfectly, and if things go wrong I accept it and take my teacher's advise (and she never seems to run out of exercises

)to improve. As she always says, if I came for lessons playing every piece perfectly she'd throw me out of the door because I wouldn't need her!!!
I now take the same attitude when playing for friends which I seem to do more and more. Again they know I've only been playing for just over 2 years and nobody has ever made a bad comment. On the contrary they're so pleased to listen to me even though what I'm playing to them is far from being perfect, but they don't seem to care!!
Last week I booked a practice room during my lunch break in a piano showroom (I've always wanted to play on a great piano so thought I'd treat myself!

). Somehow I expected the practice room to be soundproof but that wasn't the case!!! And just outside the room were 2 professional pianists testing the grand that had been tuned for some concert!!! My first tought was..shall I run away!!!

but then I thought, well, I've paid for the room for an hour, I don't know these people, I'll probably never see then again so...go for it!!!! When I left the room, the tuner and the 2 pianists smiled at me and asked me if I'd enjoyed my practice. I said I did and it was so enjoyable playing on such a great piano. They then asked me questions about my piano at home etc....I left the showroom so happy. Not once did they make me feel like I couldn't play!!! They were just happy talking to someone who enjoyed music and I felt exactly the same!
Clueless One go for it!!! Try to take a relaxed attitude. What is the worst that could happen in that concert? you mess up the piece and stop playing! What would the consequences be? Not much, the earth wouldn't stop turning, you wouldn't lose your job.... The other people would probably be willing you on to start the piece again, so it that happened start again until you get it right! As Alicia said rightly "Everyone in the audience is on your side".
This mentally has really helped me, hope it helps you too!!!
I'm sure it will go well and that you will enjoy it!!!!