Brief Answer:
Yes if it does not contain codein

Detailed Answer:
Hello Mr XXXXXXX

Cough in a child may be due to so many reasons. The main cause which must be excluded is foreign body inhalation(accidental ingestion of something which blocks the airway).

If cough is infective in origin you can use the cough syrup. But which cough syrup do you have(adult/pediatric) and what does it contain is important.
One should not use adult cough for children as it may cause overdosing.Syrup containing cough suppresent(codein) should also not to be given to children as it causes accumulation of secretion in the airway and can cause respiratory depression also.

So if there is no history of foreign body and it is pediatric formula not containing codein then you can give this in the dosage as advised by your pediatrician.

I hope this answers your query.

Regards

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