My question is what kind of OTC meds are you using? Did the ENT who did the tubes comment on it, did you ask about the sinuses while you were visiting? If you have another follow up with the ENT I would definitely see what they have to say, they are experts in that field.
I have an asthmatic son who also has allergies and has had multiple sets of tubes. His nose wouldn't always run when his ears were infected (in fact sometimes he would wake up in the morning and his ears would start draining so heavy it would be all over his shirt :( ) And it had nothing to do with milk.
The OTC stuff you use can make a difference, but if he has significant allergies something like Singulair would be best (if my son stops taking his, he is a completely different kid within about 5 days). They make sprinkle packets of Singulair for ones as little as yours, you can add into some applesauce. I would be leary of Benadryl, it's very short acting and will only knock him out until it's done working. And as he gets a bit bigger it will make him hyperactive, not sleepy, as it does my son. Claritan is ok but generally does not block enough of the allergens most people suffer from.
Also, with the problems he's having breathing at night, does he wheeze at all? Does he cough a lot at night? The cough may be from all the sinus drainage, but I really think you should get a second opinion, get some kind of prescription medication to help dry him up, and maybe even talk to a pulminologist, someone well schooled in the respiratory system if the ENT doesn't have a good answer.
I've been there and feel for you! You'll get it all worked out, just check with another ped. and see what they think. Don't stop with the doctors until your satisfied, there is no reason for you to loose sleep or for your baby to be uncomfortable like that all the time!