Dogs don't usually get colds like we do. More than likely it is a the beginning of a respiratory infection which will need antibiotics. Stress from being rehomed can make her more susceptible.
It's really a good idea to take a new puppy or rescue to your vet as soon as possible anyway to get them checked out. Heaven forbid you were to have an emergency, it's a good idea to have had your vet see her before, have all her records on file, etc. |