How can I exercise when I can't breathe?

Low and slow. Assuming no other lung or heart issues, this is likely due to not working your respiratory muscles. No different than lifting weights: I have no expectation that one can lift 200 lbs without training and working up to that level; similarly, you may also need to train your lungs and respiratory muscles to the level of exercise where you can breath more easily. Start low/go slow, progress will come.
Slow & Gradual. Aerobic/cardiovascular exercise will eventually train the lungs and the rest of the body to handle oxygen more efficiently, but must be initiated and advanced carefully in the context of chronic lung disease. Let your symptoms guide you, realize your limitations and try not to be a hero - this will keep you safe.