Yes, things can go wrong, but they're more likely to go wrong if you're worried about them going wrong.
Go in, remember to breathe, do your thing, and trust your horse; it will all get better. I was so very very nervous my first show with Rush (I'd shown before, but it was hunt seat and the horse was pretty mellow. Rush is... well, a Saddle Seat Arabian...), and he picked up on it. Last show I wasn't worried and decided that if it's going to happen, it's going to happen, and stressing won't fix anything. Likewise, he was far more relaxed with me.
Just don't forget to breathe; you'll do great! Bring photos for us :)