I adopted a dog from a shelter about a year and a half ago. He is a golden retriever/chow mix. He kept getting these horrible hot spots all over his body that looked like burns. It seemed he was constantly on prednisone and antibiotics. We finally decided to have allergy testing done on him and I am so glad we did. We never would have determined all that he was allergic to just by taking certain things away in his food. He is allergic to all meat except for fish, all grasses, all trees except for 2, soy, barley, cats, birds,dust, mold, etc. I now have him on a holistic brand food by Eagle Pak. It contains salmon, sardines, and anchovies. It sounds disgusting, but doesn't smell too badly. He is doing so much better now. I was basically poisoning him by feeding him the food I was giving him. It was a high end food, too. He still gets sores every once in a while due to seasonal allergies, but nothing like he had before.
So my suggestion is, if you haven't done it already, is to have allergy testing done. It cost me about $250 but in the long run it saved me money because every few weeks when I had to get steroids and antibiotics, it cost me $50-75 each time. I know exactly what he is allergic to and found him treats and dog food that fit his needs.

It took about 4-6 weeks to notice a difference in his skin and coat, but he is a happy dog once again(albeit a lot spoiled!)

I hope your puppy gets better in no time. Just wanted to add my 2 cents.

Chris