What Causes Runny Nose And Cough?
Likely to be a viral infection
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Most often children suffer from certain viral infections manifesting with such symptoms. If your child is otherwise active and playful you need not worry. Such viral infections usually recover in 5-7 days from the onset. You need to give your child Nasoclear Nasal Drop (saline nasal drops) one drop in each nostril whenever required, to remove nasal block. You need to give steam inhalation. Just sit with your child on your lap and place the source of steam before you. Water vapor will be in the air and your child will automatically breathe it in. It will reach deep inside and would dilute the cough. Give some antiallergic like cetirizine drops once daily for next few days and it will help in controlling the runny nose.
In case the child becomes lethargic, you would need to take him/her to a hospital without delay.
Let me know if I could help further.