Dermatillomania. It is unconscious self-harm.
I can't help you re biting but these are my tips re picking:
(1) Get several small tubes of a good (thick) hand cream. Put one in the kitchen, each hand bag, car, and bedside table. Apply throughout the day, especially after washing hands.
(2) Get a manicure set and learn to give yourself manicures. You will be much less interested in picking the skin around your nails when your fingers are manicured AND you'll find that using the skin nipper is just as cathartic as picking at the skin with your nails. The difference being that the manicure leaves your fingers much better than before, which would not be the case if you were to spend that half hour picking at them
(3) Always always have nail polish on your nails
(4) Have one of these in every hand bag, so that if you discover a bit of skin you might like to pick at, you can simply cut it off