Hello,
Thank you for asking at HCM.
I carefully read your question and understand your concern.
If the child is doing well, no
fever, he is eating and is active than the runny nose and
cough speak mostly of a viral infection and is self limiting.
I would make sure the child takes a lot of fluids so the phlegm is not thick. Also honey tea before bed might help with cough at night and also
vicks gel (with strong menthol smell) on the chest to open the airways at night.
There are different cough syrups but the one that is found effective is guaifenesine. The antihistamine you have tried and Fenestil (which is an antihistamine) are not found very effective and might make the child sleepy.
If the child is not better in a few days or new symptoms start or is any worse you need a doctor to see him.
Hope this answers to your question and is helpful to you.