Although both of my kids have the same problem this time of year (they're OK until it's time to sleep, then the drainage makes them cough and makes sleeping quite difficult)......usually it's viral and takes several days (if not a few weeks) to alleviate.
If you're really concerned, I'd recommend seeking either another visit with this pediatrician or with a different pediatrician.
I have a friend who is a Family Practitioner and for most of his life has been treated for asthma - at almost 40 years old, he finally was diagnosed with the root cause of all his respiratory problems - food allergies.
So, even the most educated people who do this day in and day out can be confused by symptoms that overlap with other things.
Good luck. I hope he gets to feeling better soon and that the meds start making everything better.