Hi and thank you for choosing H C M to post your health concern. I read carefully your question and my opinion is as follows: From what you describe it seems to me that all these paroxysms of intense coughing lasting up to several minutes, the tendency to vomit after cough(postussive vomiting) and the duration of cough(4weeks) match with the clinical presentation of pertussis infection. I dont know about your vaccination status (incomplete or absent pertussis vaccination) Pertussis is a respiratory infection that lasts about six weeks ,starting with a catarrhal phase followed by a paroxysmal phase and convalescent phase.Vaccinated adults usually develop only prolonged bronchitis.Treatment usually involves an antibiotic but it only helps if administered in the first or second week of symptoms.In your situation Ventolin inhaler that your doctor prescribed helps reducing the paroxysms and would help also if you start antitussives such as dextrometorphan,codeine.etc Another less possibility of your health problems is even the beginning of an asthma since very frequently it can be precipitated from a viral infection.It would help me to support this if i would have a well given medical history(allergies,familiar history of asthma)and physical examination Spirometry is useful for diagnosis and the treatment need to be guided by its value. I hope my opinion is help to you. Wish you good health. Kind regards Dr.Dushi