It seems that your dog may be sensitive to the new food, could have seasonal allergies, or perhaps both. You might want to switch back to the other food for a few weeks to see if things improve. Also check for fleas.
You might want to look at some of our products to address the licking. DERMA-IONX was formulated to help with allergy symptoms and provide comfort to the skin. Besides DERMA-IONX, the supplements I use along with it include Canine probiotics, vitamin C, MSM, and Omega 3,6,9. Together with DERMA-IONX it produces a synergistic effect for a faster response. I would also suggest that you give your dog only filtered water for drinking and bathing if your water contains chlorine or fluoride. Please let us know if you have any other questions.