It definately sounds like mg to me - when I cough a lot, it definitely affects my breathing. Think about what muscles you are using to cough and those you use to breathe - a lot of the same muscles are used. The more you cough, the weaker your breathing - or at least that's how it works for me.

When they tell you, you're not moving air, it is probably because your lung muscles are very weak. I find that breathing treatments help a little, but the best thing for me is a bi-pap which basically does the breathing for me until my muscles rest enough to take over on their own.

Keep following your instincts - sounds like they're sound. Good luck!