Thank you for your query on Healthcare Magic.
As your child is having GERD, the cough is due to reflux followed by vomiting might have resulted in regurgitation of feeds into pharynx and nasal airways which caused mild throat infection
as advised for GERD.
Child should be observed for increased respiratory rate
to look for any aspiration of feeds into lungs.
For cough you can give a cough drops containing mucolytic agent
like ambroxol in prescribed dose.
If there is nose block, you can instill saline nasal drops into nostrils.
I advise you to consult pediatrician
for the examination of the child and for prescription of medication.
Hope I have answered your query.