Oh wow.. i'm so sorry your going through this. I had a somewhat similiar experience with my newest addition not very long ago. She had a URI, and eye infection and coccaida.. not to mention she was flea infested. She is doing wonderfully right now but there is no way I would have returned her after the 2nd I got her.
I would assume that the antibiotics are for the cough.. did the vet give you an ointment or say what the skin problem was caused from? If it is curable and I was in your shoes I would just treat it, it's so hard when your attached but at the same time knowing that you provided income for someone who isn't the type of breeder you intended to buy your pup from.
I just re-read what the vet said about the skin and that you have a shampoo for it. As long as your little one's hair will grow back everything sounds treatable so if your attached I think you already know what you will do
