Argh, I hated school dances of any sort, not just prom. I believe I attended two in all my years at school; they were so awkward and most of the music was dreadful. Thankfully at 27 I don't have to worry about those things now.

I'd much rather spend a relatively quiet evening out at a pub with a friend or two, enjoying a few drinks and some live music.
As far as advice... I'm not sure I have anything too useful. :\ How long is the evening going to be? Is it required that you be there for the whole thing? (Of course, possibly you want to be there for the full duration of the event...)
Oh! One thing comes to mind actually, though it's maybe not directly helpful as far as attending the prom itself. When I was 19, a very extroverted friend of mine who absolutely loves clubbing and dancing and tons of socialising dragged me to a club in Toronto one evening. I'd never been to a club before and figured I might as well push my boundaries a bit and see if I could enjoy myself. The music ended up being awful and I got very drunk in an attempt to make myself more comfortable and feel at ease, and... well, let's just say I don't like to recall that night. (Hopefully you don't end up feeling that way about prom, though!) I felt so out of my element and very uncomfortable with my behaviour when I was sobered up the next morning. What I did to help ease that feeling was to leave my friend's place early in the morning and spend the day on my own -- taking time for myself and making extra effort to fill that time with things that helped me recharge and feel in touch with
me again. If I recall correctly, I spent the day exploring one of the waterfront parks in Toronto and then hung out at a bookstore for a while, got a cup of tea somewhere and sat reading for a bit, and took the train home in the early evening and listened to favourite music the entire way back. Basically, I contrasted the previous night's very intense socialising (well, intense for
me, haha) with a low-key but very fulfilling day spent by myself. I felt so much better after doing that.
I'm not sure if that's useful to you at all... but I would suggest that you do something the next day that helps you recharge and sort of just come down from all the activity the night before.
P.S. I hope you have a fun evening! Good luck.

Don't put too much pressure on yourself, if that's possible.