A.L.
I wouldn't stop breastfeeding, but there is some credibility to avoiding the milk. MIlk can actually thicken the plegm, unless he is otherwise well hydrated. Water will help thin it out a little, though, so I would continue the breastfeeding, and give hime water (or heavily diluted clear juices - think apple or white grape) to drink other times.
Also, we have had some luck with using the freezer to stop those bad coughing fits. Inflammation makes it harder to breathe, so just hold him in front of the open freezer, and let him take deep breaths of the cold air. It'll help calm the coughing fits, not long, but hopefully long enough to fall back to sleep. Steam will help calm a coughing fit, too, but the safest way is to steam the whole room (don't hold him directly in front of a tea kettle or warm mist humidifier!); it takes a lot longer to steam up the bathroom, than it does to just open the freezer door.