Most coughs are viral and will resolve on their own.

But simple remedies to apply are to exclusively breastfeed, keeping baby warm by avoiding unnecessary baths, once daily is okay. Avoidance of smoke and people with cough and catarrh. No need for medications but if the child should develop breathing difficulties kindly take to see a pediatrician.

Is your child not over dressed?

Is the room temperature cool enough?

Is child sweating in an environment where others are not?

If yes to the above questions you will have to take your child to see a paediatric endocrinologist for evaluation and management.