P.W.
It could be he just hasn't been on antibiotic long enough. My now adult son had ear infection after ear infection at that age. Finally they admitted him to the hospital and put him on an antibiotic drip for 3 or 4 days to get rid of the bacteria. You might ask about that.
Get the baby on vitamins and a probiotic. I sell vitamins with a prebiotic that are wonderful. I agree that you would do good building his immune system. More than likely he has allergies that are irritating his sinus and leading to infection. You can fight the allergies by building his immunities.
I don't remember reading whether you are using a humidfier. Another thought.
Good luck today. Please let us know what the specialist says.
P.