I had a similar problem with my dalmatian, Molly, who has since passed away. When she was 6 months old, the allergies started. She had the testing and de-sensitizing shots and I spent a small fortune on her and a skin specialist, customized serums and shots. She too, would chew the pads off her feet, have unending ear infections and general itchy skin. She was allergic to almost everything. She was on Eukanuba fish and potato food which was the only food I found that she tolerated. Unfortunately, the de-sensitizing shots did little for her. We ended up putting her on prednisone for life, but just a small amount daily and after fully researching the side affects. It was a last resort and we went for comfort and quality of life for her. She lived in peace to 11 years old.
Many people are totally against prednisone but in severe cases, it is a miracle drug. Hopefully you'll have better luck than we did if it is in fact, allergies.