You might want to look at some of our products to help the skin. DERMA-IONX which is an oral homeopathic product stimulates the enzyme systems in the body which reduces itching and inflammation, promotes healing of the skin and helps with assimilation of nutritional components in diet and supplements. I would give 10 drops twice daily on the breakfast and supper canned food. In addition I would give Kali Bich 200C every other night at bedtime for 6 weeks. If you cannot find that potency you might try Kali Bich 30C instead. Your health food store should have it.
The supplements I use along with DERMA-IONX include PROBIOTICS and OMEGA 3,6,9. Together with DERMA-IONX it produces a synergistic effect. I would also suggest that you give your cat only filtered water for drinking and bathing if your water contains chlorine or fluoride. As for diet, if your cat is not allergic to these protein sources you might try a fish or turkey based grain free food if your cat is quite warm and seeks cool places. These foods are considered to be cooling according to Chinese food therapy. You would want to avoid chicken or lamb which are warming for the skin if it is already too warm. Beef is neutral. Avoid treats that have artificial colorings.