It may be time for a diet change. I fed Medi-cal dog food to my dogs in the past, I was horrified at the ingredients when I later learned how to really read them
You might want to start on a good quality dog food which has good quality protein sources. There should also be more than one protein source and a grain should never be the number one ingredient. I like foods like Natura, Wellness, Solid Gold etc. You could also give your dog a little variety in his diet. I find this is the mistake many people make, choosing one dog food brand and sticking with it for too long. You might want to add some good oils like Hemp seed oil (which has a perfect ratio of Omega 3,6 and 9 fatty acids). I like to add sardines and canned wild salmon to their food as well. You might even want to substitute a few meals with a home made diet, if you cook the meat then add some digestive enzymes and I would also add probiotics for gut health.
Also make sure you are brushing your dogs coat and are distributing the oils throughout the coat. I have seen dogs get dander as well after a bad bath where the person did not get all the shampoo out.
My Rottweiler has almost the same coat type as a Lab. She gets dander during the changing seasons when her coat is blowing out. Make sure you are brushing your dog to get all the old coat out, pick up a shedding blade. I also found that the winter zapped a lot of moisture out of her coat, then come nicer weather it some times gets a tad bit more oily.
Of course, the other advise you received is good. You may want to have a vet look your dog over just in case it is a medical reason.