Thanks for posting your query.
Productive cough is due to upper respiratory infection
) which is usually viral but it can bacterial. Irritation of airway cause cough and excessive mucus formation which is normal protective response of body to get rid off causative agent. You should also notify your doctor if you have allergies which may cause sore throat
and runny nose. Usually antibiotics do not work in viral infections and it resolves on its own. Treatment prescribed by your doctor suggests you have COPD or asthma.
Take plenty of water.
may soothe your throat.
Humidifier may help you.
Get your chest X-ray and talk to your doctor for further management.
Hope it helps.