Have you seen a lung specialist? It could be something like asthma, from what I was reading, but there are many other things that can give this image in x-rays. I would head to a lung specialist if I were you...if you haven't already. I wouldn't fool around with that.
Austen is correct in saying that fibromyalgia is not an inflammatory illness.
Please let us know what you find out and don't stop searching. Coughing like that is horrible. I use Mucinex DM for bad coughs and you might ask your doctor about that. The DM stands for dextromethorphan and it's a cough suppressant so you aren't coughing all of the time. But when you do cough, it's a productive cough.
Sherrine