I have a lab mix that had the same problem. Tried the drugs, didn’t work. Went to a good dog food, grain free. Didn’t work. Shampooed her with a specialty shampoo. Didn’t work. Started giving her an oatmeal bath once a week: Mixed up 2 parts oatmeal and 1 part baking soda with water until you get the consistency of … well… oatmeal, then crawl into a lukewarm bathtub with your dog and spread it on her coat. Rub it in, and then just have a spa time for about ten minutes. (It needs to sit on her skin for that long.) Rinse off and dry like normal.
We also added a teaspoon of coconut oil to her food once a day.
Her skin has completely cleared up and her coat is thick.
Every year around late Spring, she starts having the problem again, so we go through our spa routine and it heals right up.

Please heed the advice of those saying “rescue”. I just rescued an 11 month old lab mix and she is aawesome. She was very forlorn in her cage. Now she shines with happiness, and she loves me without question. She came to us potty trained, with basic commands, and crate trained. You will have to do all that yourself with a puppy. Best of luck!