Boarding a 13 week old puppy is not even an option! In order to board, you need to have your dog fully vaccinated including bordatella. Sounds like you are having a little buyers remorse about your purchase. Personally, I would be a little concerned what would happen to the puppy if it were returned to the petshop.
Did the petshop cover the vet expenses with some type of guarantee? If not I would be asking for a refund and as Elaine said looking into the puppy Lemon Laws in your state.