Hello and hope you are doing well.
Cough, chest tightness and breathlessness the three symptoms 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. Your symptoms could also be due to COPD or Bronchiectasis. The other causes could be due to Bronchitis or Cystic fibrosis. 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 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.
Time to see the doctor. Waiting too long can lead to lung problems.