He might have a Doggie cold (respiratory virus), or he might have Kennel Cough (which is just a specific type of Doggie cold virus).
If your first Vet can't figure it out, then I guess I would try another Vet. Make sure you don't pre-diagnose the condition before letting the vet think about it, sometimes that causes them to put blinders on when figuring out the problem. I would just take the dog to a good vet and say, "the dog does this, that and the other thing, and I'm worried about it, can you help". Then let the Vet figure out what it causing it.