Our little 4 lb chihuahua / minpin started out pretty rough. She was not taken care of, left out in the Texas heat, had fleas, worms and puppy mange with spots of fur missing and sores on her. The vet gave her some meds that got rid of the mange but caused another skin problem. We took her off that and bought baby diaper rash med - Desitin multi purpose ointment. It is clear. Started rubbing her down with it and all her fur is back now.
Hope your baby gets better soon.