Hi... you might wanna try the remedies suggested in this article https://sg.theasianparent.com/singapore-mum-home-remedy-for-babys-cough
Try sunctioning nasal mucus and keeping the air moist. Cough and cold medications generally should be avoided in babies.
It could be that the air he is exposed to is too dry. Maybe too much aircond.
Lala Ling