what you posted... why would you believe your dog has sarcoptic mange?

A little bit betta won't cut it for flea infestations. Quite possibly the dog has an allergic reaction to the flea bites by now. First you need to get rid of the fleas. Go to the Vet and ask for Capstar. Time to shampoo your carpets. You can then try something like Program until all fleas are gone from dog and house. After that a monthly treatment with frontline.

P.S. Color of hair has no relationship to oil content of a dog's skin.