When you are sitting the trot, try to sing out loud or at least count out loud. This will keep you breathing and keep your mind and body from freezing up.
Great advice! Also remember to relax and move with the horse, the more you stiffen up, the more likely you will be to fall. This might seem odd, but try to keep a running discussion with yourself in your head, especially if you get nervous: "I'M going to FALL! Wait...not ON MY WATCH! Heels down, relax, move with the horse, smile, you call this riding?!" It's saved me a few times, but I may just be a weirdo
I would also invest in some lungeline lessons and go somewhere where they will let you keep your arms off to the side. This tends to get rid of bad habits pretty quickly, I wish we had places that let you do that around here.