Welcome to YT
! No, there shouldn't really be an audible breathing sound except perhaps some snoring in some dogs/yorkies. Is this a puppy...? If yes, did the puppy recently have a kennel cough vaccine or anything? They can actually contract kennel cough from the vaccines. So I'm not sure if that's what you're hearing or not. If the sound is really obvious/odd - I'd most definitely get to a vet. Make you sure you videotape that breathing/sound on your phone so you can show your vet.