Is tongue/cheek/lip biting a dermatophagia or self injury?

A little of both...: Intra-oral biting can be strictly conscious, strictly compulsive or a combination. In any of these cases it could be construed as both dermatophagia and self-injury in varying degrees as technically dermatophagia is self-injury even though it is classified as form of (obsessive-compulsive) disorder. Don't confuse this with accidental intra-oral bites which may be self or externally inflicted.

Biting: If you have broken down dentition, you might cause trauma to your tongue and cheek as well.