My relative had this problem. She's 45 years old and was a compulsive nailbiter and skin picker especially around her nails. Her fingers and nails were in a very sorry state. She tried Bach Flower Remedies. The remedies she took were Agrimony, Beech, Cherry Plum, White Chestnut and Chestnut Bud (Look up www.bachcentre.com for details on the remedies).
In two weeks, there was a major improvement. Her nails were no longer bitten to the quick. The skin around them started looking healthy with less picking. Even better, her family reported great improvement in her moods and behaviour. Now after 6 weeks her hands are looking normal. She intends continuing BFR as she feels "lighter".
I know BFR are person specific and address a person's emotional state. These ones may not be the best fit for another person. Still I hope this may be of some help to someone.
I remember someone mentioning inositol helping with their skin picking. It may be worth a try.