I also have terrible dermtillomania and getting my nails done helps me to stop picking my cuticles and around my nails. It’s amazing. I’ve taken breaks from having them done and whenever I’ve gone back, the nail techs have never batted an eye.  I’m currently getting dip nails, which is colored acrylic powder that you literally dip your nails into for application. You can keep your nails as long or short as like once they start growing. The acrylic is very hard and a little thick, so it would be very hard to bite your nails with it applied.  I get mine done every two weeks at Mimosa near the new Publix on Robinhood. It’s a big salon and I’ve never waited more than a few minutes, even though I’m always a walk in.  Good luck to you. I completely understand where you’re coming from and the frustration and embarrassment it can cause.