Did your vet do a culture and sensitivity test to see what kind of RI your Cham has and which meds would work on the type of infection your Cham has? Not all antibiotics work on all RI's. Some RI are contagious. You would need to know the type of RI he has to know if it's contagious.
I would not worry about air born infection, I would though clean the cage bottoms with separate paper towels, and not move feeders from one cage to the other.
These are practices that should be followed URI or not.