It could be either, but because there was congestion present that the antibiotic took care of, it is likely that part or all of it is kennel cough.
Clavamox is not a great choice for this. Not a big surprise that it didn't seem to work. Also though, antibiotics don't cure kennel cough, but do take care of secondary infections. The cough could take weeks to go away. I just went through the same thing with my puppy earlier this year. It kind of sounded like CT, but then he got all nasally, so we knew it was KC. Treated with antibiotics for the secondary infection, stopped the nasally-ness, and eventaully got rid of the cough. He gave the same thing to my Yorkie and it was the same story with her.
Doxycycline is a good antibiotic for this; however, it usually isn't given to puppies. It is very possible that your pup will have yellow staining on the teeth now because the adults aren't fully erupted (so just fyi).
Was an xray done? That could help rule out CT. If the vet is that concerned, then maybe it's time to see a specialist or see another vet at the least. Your explanation of the symptoms sounds like KC to me, but of course always err on the side of caution with CT prone breeds.
__________________ Crystal  , Ellie May (RIP)  , Rylee Finnegan  , and Gracie Boo🐶 |