Thanks for posting your query.
From the medications that your son has been prescribed, steroid
, I assume he has been diagnosed to have an allergic or asthmatic cough.
You can continue the medications for 5 days. If cough persists, then he needs to be checked for other reasons like infection like laryngitis
, post nasal drip
In the meantime, try to make him comfortable with the following measures:
Give him plenty of water or fruit juices to keep him well hydrated.
Give him 1 teaspoon of honey twice a day.
Encourage him to gargle with warm saline about three times a day.