Your child is being treated for sinusitis
with an antibiotic.
Children of this age can usually cough out their sputum so you can ascertain whether it is dry or wet cough. It usually takes time for the secretions to get completely cleared in a sinus infection
If you feel the cough has worsened and fever is persisting, it would be advisable to get an x ray
PNS to determine the extent and involvement of sinuses
If x ray is suggestive of the same, the antibiotic can be changed accordingly.
So get an appointment with your Pediatrician
to get him reviewed.