If it were me, I would have him tested for pertussis. Infants with pertussis do not always exhibit the characteristic whoop and it is commonly misdiagnosed as asthma, pneumonia and bronchitis - VERY commonly. Even more so when a child has been vaccinated, for two reasons: First, they automatically rule out pertussis, just because the child's been vaccinated, even though that vaccine is less than 70% effective, meaning 1/3 of babies who are vaccinated will not be immune. Second, because vaccination can change the characteristics of the illness.
It probably isn't pertussis, but I really would have him tested if I were you, because it's possible and I would want to make absolute certain that they hadn't just gotten it wrong. The reason being that if it is pertussis, those medications won't help and could actually make it worse. That's just what I would do if I were in your shoes, after seeing how inept doctors are at dxing pertussis when I had it and when my DD had it.
I would also start giving him powdered Vitamin C. You can mix a pinch of it with breastmilk or formula if you can't pump anymore.