Check temperature. I agree that most likely you do not have bacterial pneumonia which some patients develop following a viral infection. Viruses may cause damage to the lining of the airway. In the meantime, a humidifier and staying well hydrated, while recovering are suggested. If you have problems breathing and/or fever, please see your physician. If the cough lasts longer than 3 weeks, follow up is advised.
Influenza. This virus causes loss of cellular tissues in the trachea and bronchi which may persist until there is regrowth of these elements which provide protection to the airways. Yes, this may be bronchitis, but doubt that it needs further treatment unless you have trouble breathing, you begin having changes in the sputum, develop fever or other symptoms occur. Hope you get better soon.