Well, now I know why all of the above wasn't working. He has a sinus infection!
Who knows how long he's had it. Poor little guy. Just like his dad, he doesn't complain when he is sick. I had no idea. The only symptom he showed was the cough, plus he started hitting his head with both hands (like "I coulda had a V8!" but hitting both temples at the same time). The allergist noticed a rattle in his chest (which I noticed too, but only just that day) that he said was not a wheeze (ie, don't need to worry about asthma just yet) but a mucous-y rattle.
He's put him on antibiotics for two weeks, plus we are to use our nebulizer (which we purchased when Kibi came down with RSV at 7 months of age - poor thing!) to administer Xoponex via breathing treatments twice a day for the next week, "as a booster," the allergist said.
Well, I hope this works. Hopefully we can knock out this infection and get the poor little guy cleared up once and for all.
(By the way, the allergist confirmed that pollen season is over in the DC area! Halleluiah!)