Dampness alone wont start a bird coughing or you wouldn't be able to explain how I have never heard a chicken cough once in the going on four years I've had them. Is the coop itself dry inside? If so, dampness probably isn't a cause, though it can contribute to their weakened state and they can then catch a disease.. I agree that you should not use antibiotics, partly because you have no idea what you're dealing with. Have you added any new birds lately? I'd make sure the coop is dry, separate any that are coughing or congested from the rest, keep them warm, give extra protein and some unfiltered Apple Cider Vinegar (2 tbsp to one gallon) in their water, but not a metal waterer. Then observe them and the others. If they get really bad, I'd cull them. If they recover, maybe it was something environmental. So many diseases make them carriers for life and antibiotics may only make things worse by creating resistance if they are used incorrectly, i.e., antibiotics used for a virus are useless anyway. My own policy is to never treat anything respiratory if it ever crops up.
