Most cold and cough both in children and adults are caused by viruses which will run their course with or without any medication.

On what to do..
✔ keep baby warm
✅ if there is fever Pls uncover the baby and give paracetamol in appropriate dose or Tepid sponge to bring the temperature down
✅ you can do steam inhalation with your baby (both mother and baby or father and baby). Never leave baby alone on steam inhalation
If nose is congested, u can give saline drop in each nostrils to help decongestant the nostril.
✔ if you have a room heater, you can use it to make breathing easier for your baby.
✔ continue breastfeeding baby EXCLUSIVELY.