Due to a postnasal discharge I suffer from irritating trachea which in turn makes me constant coughing. What should I do?

Several possibilties. The nose produces about a quart of mucus a day which by ciliary action goes down the back of your throat. The following possibilities need to be ruled out. 1.) nasal allergy, 2.) non-allergic rhinitis, 3. Rhino-sinusitis. 4.) nasal polyposis, 5.) adenoiditis. (inflammation-of the back of nose). Thus, you need a diagnosis. See an ENT doctor. Bottom line, you need to identify the cause of pnd.