Me & show nerves have a love/hate relationship. On the one hand, they are annoying and make me tense up and forget things. On the other hand, if you harness them sort of use that energy, you can concentrate intensely and have the best ride of your life! It's funny when people don't understand why I would get nervous for a show/comp, but it really is life/death to me! :)
One thing that might help is to realize you are SHOWING your horse. You're trying to make the horse look good, no one cares about you as the riders. Think about them only focusing on the horse.
Breathe! When memorizing a pattern, figure out when you are going to take breaths. ie: circle, lead change, breate, back to trot, breathe, walk.. etc.
Before you go in, take some deep breaths and smile! It's for fun, after all :) Maybe hum a song or "listen" to one in your head.
For better memorization, draw the pattern over and over again. If it has obstacles/jumps, go into the arena and visualize your ride. What I do a lot of times (because I literally have to do something before I truly learn it) is find a spot big enough to walk your pattern yourself, like pretending to be the horse ;)
Every great dream begins with a dreamer. Always remember, you have within you the strength, the patience, and the passion to reach for the stars to change the world. ~Harriet Tubman