I do the same thing! But that's just one of the many OCD tendencies I have. Have you ever tried CBT or DBT? Maybe you could ask your doctor about it.

One thing I have been doing is setting aside specific time each week to do my nails. I find that if I go get them done somewhere they don't do a good enough job on getting all of the dead skin off. Then during the week when I notice myself gnawing on my fingers I stop, pop a piece of gum in my mouth and put some lotion on my hands. Lotion tastes icky. Also I make sure to keep my hands moisturized especially the cuticles. Burt's Bees makes a lemon cuticle balm that works very good.

Good luck.