Hello and hope you are doing well.
As suggested above your symptoms could be due to Asthma. Cough, chest tightness and breathlessness t are the triad of symptoms for Asthma. It is a disease affecting the lungs causing narrowing of the airways, usually due to an allergic reaction to triggering factors. Therapy is with bronchodilators which cause the airways to dilate. You will need to consult your doctor who may need to do a sputum culture and sensitivity to determine what antibiotic the organism is susceptible to. He may even ask for repeat blood test and an X ray. Lung function tests could further help in evaluation. In the meantime take OTC acetaminophen, try to take warm oral fluids and do steam inhalations prior to your meals. This helps to loosen up and bring out the secretions
Hope this helped and do keep us posted.
I'm not a doctor, but I think it's either asthma or some other allergy.
You need to get a new doctor, as the ones you mention are being negligent, not practicing due diligence in diagnostic testing to determine the cause of your cough for the most effective treatment.
For example, did they fail to send you to an allergist for testing to see if you have any severe allergants that you should be avoiding if indeed severe chronic coughing is an allergy symptom in your case?
Did they not suggest they refer you to a pulmonary specialist for lung function testing?
Do they say you have chronic bronchitis?
Have they checked you for acid reflux, which can cause coughing?
Your chest x-rays at the time were fine, but did they not do TB skin testing at that time as well?
Have they enquired as to your stress levels?