Yes, puppy milk could be making her itchy, as most adult dogs have a lactose intolereance. Apparently puppies produce rennet, which adult dogs don't. Rennet is used to make cheese, which is why adult dogs can tolerate cheese more than milk and why puppies can tolerate milk. Rennet is also what gives pups 'puppy breath'. She does not need milk.

Also, what food is she on? Lots of dogs are allergic to maize or wheat and that often exhibits itself as dry, flakey skin.