Rhinitis may also be allergic rhinitis.
Allergic rhinitis and asthma are brothers.
"Once you cough, it takes about a month to get well"-probably seasonal.
Diagnosis-shows that asthma treatment is effective. The technical term is FEV 1 increase 15% or more after inhalation of airway dilator. (There are other ways, of course)
Treatment: Get rid of allergic environment and reduce exposure to allergens. Inhale surface hormone (fluoxetine), airway dilator (Vantorin),
Or inhale nimesulide directly.
After all, I didn't see the patient. For reference only. It is recommended to consult a respiratory doctor.