There's always the option of going stag. I forgot about having to show up for my own prom one year until the florist delivered the corsages the afternoon of that day and then I remembered that I did indeed have a prom to attend!
Of course, I had no dress to wear..but I did have a corset and a tux so I decided to wear what I had on hand, and prepped in record time.
So I hopped in the limo, stag, and with the full intention of just going to be myself and have a good time. I wasn't pressured to stay with my date, to make sure s/he was doing alright. I was able to dance with whoever I felt like, and really it all just ended up being one big party. Not to mention that I ended up getting asked out to about 4 other proms later that month as a result...
The point is, the prom isn't like a black tie ball where all the formalities and social civilities are the be-all and end-all. It's an event from which you'll have memories that you'll one day look back and laugh. Just go, ace that test, and have fun. You never know what happens. The girl in question might ask you out instead upon hearing reports of how well you did at the prom!