Our newf had the same symptoms that you dog has. We found that she was allergic to eggs, in the food she was eating there was dried egg, so we switched her to a food that had whole eggs thinking there would be a difference, some bit better, but still there, so we switched her to a fish formula with no egg and now she is doing great, no itching and no hair loss. She is only shedding like she is supposed to. We tried the fish oil as well, it did help, but maybe there is an underlying reaction to something in the food. We were lucky the food she had been on had the exact same ingredients, in a different order, but when we changed to the adult from the puppy there was egg in the adult formula and not in the puppy. So it was very easy for us to find out what the allergy was.
The vet can run allergy tests to find out what she could be allergic to. Good luck.