It's totally normal not to want to show! I don't like showing either, to be honest. I've been riding for over a decade now and love riding jumpers, but I don't have a strong desire to get into the show ring. I don't get overly nervous about the crowds, but I do get the jitters.
Riding isn't about showing. If you don't want to, then don't. There are other much less competitive events you can with your horse if you still want to do something fun. If not, just enjoy whatever you do with your horse now. That's the best thing about this sport, you can decide!
"Donít be the rider who gallops all night and never sees the horse that is beneath him."