its not just cleaning himself he does it for about two hours
my Jack russle does that also to where he licks them raw, i put benadryl on his feet.
First have a vet check your puppy to make sure there are no imbedded foreign objects. Over-grooming can be a stress response. It might also be an allergy. Read here. Good luck.
Maybe they just taste good. Maybe he just likes the feeling.
Maybe it’s a cat, not a Yorky.
http://www.fluther.com/disc/17881/my-dachshund-biteschews-his-toenails-is-this-normal/