It's possible that your puppy is troubled by allergies, and this is causing his runny nose. Run a humidifier/vaporizer in the room he spends the most time in, and also steam up your bathroom with a hot shower and sit in there with him for about 10 minutes, every few hours, to help open up his nasal passages and decongest him. Wrap him in a towel before coming out, so he doesn't get a chill.
If his runny nose continues, it may be due to teething issues, as he's approaching the age when he'll be losing his 'milk' teeth and his permanent ones will be coming in. This process takes a few months to complete.
I'm very glad you've already had him to the vet for evaluation, and if he continues to act normally, eating, drinking, eliminating, and is active and alert, that's great. However, if his nose continues to be runny, put a call in to the vet and ask what further can be done at this time, to help him feel more comfortable. A runny nose may be the precursor to an upper respiratory infection, or kennel cough. If the discharge is clear, there's less to worry about; if the nasal discharge is yellowish or green, this indicates infection.
I hope all will be well!