I remember my basenji with runny nose when he was a 5 months old puppy, so we took him to the vet. He had found a slight infection on the bronchus, nothing really serious and everything turn well after a short treatment but it would be good if your vet could take a look at it better.
It is clear and very little, and like I said, not constant. It was pretty chilly in the house when it was running, but after I warmed it up in here, it stopped again. Not sure if it was a coincidence, but I'll keep an eye on it and mention it at the vet.
Xander had a drippy nose when we picked up Gambit, but it was just the stress of having a new dog and stopped after about an hour. Our whippets get drippy noses and sometimes squinty eyes at this time of yr when the grasses are just starting to poke thru. I've taken them in to the vet before and he said its seasonal allergies, I believe the last time a bendryl was the cure. The vet can give you more info, reminds me I need to make my appt for the 3rd shots for my girl too.