This sounds like what my daughter is facing. She too has had a runny nose for almost 2 months now and despite 2 rounds of anitbiotics and antihistamines, there has been no improvement. My Paed referred me to a paediatric ENT and an X-ray showed that she has congested adenoids. If she does not improve by next week, he says he will need to scrape some cells off.
The reason for this is that for some kids, their adenoids (which swell to fight off infection) do not shrink back to thier original size when the infection is over. This causes the blocked, runny nose which leads to mouth breathing (which attracts more infections!), snoring and if left untreated, the child can suffer from poor learning abilities since the child cannot breathe well or sleep well.
I'm no expert, just repeating what the doctor explained. I would suggest that you see your paed.
My friend told me of a child who snored very loudly and had the symptoms you describe. After he had his adenoids removed, he improved tremendously... spoke better, breathed better and slept better too.