Poor baby! Sounds like kennel cough! After my mom adopted Cookie last year (5 year old small bred mix from the local shelter) she took her to the vet for an exam, my mom had noticed her coughing and brought it up to her vet. My mom's vet said it was kennel cough but there really wasn't anything to prescribe, that it would just go away on it's own like a human cold. And it did, it just went away!