Thank you for your query,
This chronic cough
, mostly worsening during nights may be due to the gastrocolic relux disease as the reflux causes microaspirations into trachea during the nights and causes cough.
So my suggestion is to evaluate for gastroesophageal reflux disease
and to start a trial regiment treatment for it to assess the reponse.
Consult your Pediatrician
and discuss with him.
Hope I have answered your query.