I had no idea there was such a place "Cough Clinic. I going to make an appointment today. Thank you.
Yvetta
The hard cough alone could be the cause of your “severe backache between shoulder blades” as could also many physical activities, such as heavy lifting, that could put a strain on your back muscles. That is most likely since, I assume, the X-rays and CT scan showed no other abnormalities, and your statement “when my breathing is ok, I don’t have the back pain.”
I note the mention of COPD below. That is unlikely, since you “don’t smoke” and the diagnosis of asthma would be a much more likely diagnosis. I can only say that there are very many causes of the type of cough you have; sometimes the best approach is to seek care at a hospital Cough Clinic, staffed by doctors with a strong interest in and experience with the causes and management of cough. If what you say, “the doctors have no idea what’s wrong with me”, your best chance would be to arrange to be seen by a lung specialist, ideally in a cough clinic. Since you live in Colorado, your best bet would be either at National Jewish Health or at the University of Colorado Hospital Clinic.
I am sorry I can’t be any more specific, but that is the nature of cough diagnosis and treatment.
Good luck