Corn is probably what is causing the itch. There are lots of good doggie foods without those bad ingredients. You want something with human-grade ingredients. I feed Natural Balance Ultra-Premium Small Bites. She also likes Wellness, but the chunks are really too big for her for some reason. Another good one is Canadae. And now my mind is blank on any others. Forgive me!
I also bake white chicken breast and feed that with her food as well.