Chicken-free dog food?

Screech is my foster dog. He has alopecia and his hair fell out of his face and sometimes it thins elsewhere. When we first got him, we fed him regular cheap dog food and his fair fell out a lot. I read something that said he might have a grain allergy, so I got him turkey based grain free food, I think Rachael Ray Nutrish brand. His hair didn't grow back in his face, but the rest of his coat started to look healthy. One roommate bought that kind twice more, and still it was fine. Then I read Please Stop Buying Your Pets Grain-free Food in Slate which said most animals aren't actually allergic to grain but to a protein. Around the same time, my roommate bought a new bag of the Nutrish, but chicken-based instead of turkey. Screech just finished that 25 pound bag, and his hair is thinning everywhere again.

I went to Ozzie's (formerly Associated), Bravo, C-Town, and Key Food. All the dog foods have chicken except fancy grain-free kinds. So I ended up buying a salmon and rice bag that was $16 for 4.5 lbs. That is more money per pound than I spend on my food! But I don't know what kind of food to get him. Maybe back to the old Nutrish with turkey.