Aloha! You're speaking to Dr. Michael Salkin
Biting at the paws is pathognomonic (specifically indicative) of both atopy
- allergies to environmental allergens such as pollens, molds, dust, and dust mites, etc. - and, less commonly, food intolerance. Both types of allergic dermatitis
can cause generalized pruritis (itchiness) and the skin changes you're seeing on her back. It's important to note, too, that secondary infection by both bacteria and yeast (Malassezia) are commonly seen with an allergic dermatitis and those infections will compound her pruritis and irritation.
Her vet will need to perform skin scrapings of affected skin in order to rule in or out an underlying demodicosis
(Demodex mange mite) and perform a cytology - microscopic exam of a small sample of the skin surface - looking for abnormal numbers of bacteria and yeast - and then treat predicated upon the findings of such testing.
In most cases of atopy a short course of a corticosteroid such as prednisone is prescribed. Food intolerance is addressed differently...
Food intolerance/allergy is addressed with prescription hypoallergenic
diets. These special foods contain just one novel (rabbit, duck, e.g.) animal protein or proteins that have been chemically altered (hydrolyzed) to the point that her immune system doesn't "see" anything to be allergic to. The over the counter hypoallergenic foods too often contain proteins not listed on the label - soy is a common one - and these proteins would confound our evaluation of the efficacy of the hypoallergenic diet. The prescription foods are available from her vet. There are many novel protein foods and a prototypical hydrolyzed protein food is Hill’s Prescription Diet z/d ultra (my preference). A positive response is usually seen within a few weeks if we’ve eliminated the offending food allergen. Food intolerance can arise at any age and even after our patient has been eating the same food for quite some time.
Finally, because she's a schnauzer we must always consider the comedo syndrome when the backs of this breed are involved in a skin condition. The schnauzer comedo syndrome is a common acne-like disorder of follicular keratinization causing few to many nonpainful, nonpruritic comedones (blackheads) and crusted papules. Please let me know if you're seeing such blackheads.