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Assuming that your baby has no other symptoms such as fever or runny nose accompanying the cough, my understanding is that this is a very simple issue of post nasal drip aggravating the gag reflex. This means that nasal secretions flow back into the throat causing a continuous cough like response.
My suggestion would be to make the baby sleep with the head on an elevated surface as a pillow and also please avoid cold beverages and citrus foods, particularly after 5 PM.
Try this for two to three days. If any symptoms arise please feel free to ask me.
For more information consult a paediatrician online --> https://www.icliniq.com/ask-a-doctor-online/paediatrician