Itching can be caused by a plethora of different things from a food allergy to mange. At minimum, I would have your vet do a skin scraping to determine if this is a bacterial infection. Demodectic Mange stikes young pups, so I would have this possibility eliminated as soon as possible.
Some dogs have a severe allergy to corn or beef products. A holistic dog food is the way to go if this is the problem. Eagle Pack brand dog foods make a wonderful variety of foods to aid if this is the problem.
I wish you all the luck with your puppy and hope she feels better very soon :)
animal care specialist
animal care 15+ years