I would say yes, you have Dermotillomania...not sure if that's spelled right. :P I looked up some terms online:

Skin Picking: dermatillomania
Skin Biting: dermatophagia
Nail Biting: onychophagia

Personallity, I suffer from all three of these. I bite/pick at my nails, then eat them. I hardly have any nails at all! I also bite/pick at my skin, eat that...and likewise with scabs...especially on my face. :P

About 25% of those with OCD have some form of this, so it's quite common! It's also very hard to stop.