Any suggestions on what brands/kinds of dog food to feed an adult Chinese Shar-Pei?

I have an adult female Chinese Shar-Pei that is a little over one years old. I originally got her from a couple who could no longer care for her. She is an outstanding dog with a great personality and I instantly fell in love with her. I had noticed just a few minor issues with her though. She seemed to be underweight and had a very light skin irritation. I believe it had a lot to do with the type of food her previous owners were feeding her, which was an unheard of brand from a local dollar store. It seems like the dog maybe had obtained an allergic reaction from this food. Her skin was very dry, flaky, itchy, swelled up and pinkish. Also she was losing some hair on her lower back down by her tail. I switched her food to a brand called Nature's Recipe in particular the flavor Easy-To-Digest Chicken & Barley. This is suppose to be an organic food for dogs. I use to feed this same food to a different Shar-Pei I use to own a while back and she did great on it. Problem I'm having with the current Shar-Pei I own now is that she does eat a lot of it, but still has not gained any extra weight that I can see. Her skin is no longer dry, but is extremely oily now and it's causing her to become very dirty fast. After a week of being on this food she needed to be bathed again only a week from her last bath because she smelled. Although she had stopped itching and the swelling/pinkness of her skin calmed down, I still don't think this is the best food for her. Chinese Shar-Pei's are well-known to have sensitive stomachs and food allergies. I am just looking for some suggestions on what different foods I might could consider using for her. If there are any other Shar-Pei owners out there that can lend some helpful advice, please feel free to comment below. Thanks!