Try keep baby warm, if there is fever please 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, you can give saline drop in each nostrils to help decongest the nostril. If you have a room heater, you can use it to make breathing easier for your baby. Continue breastfeeding baby exclusively If the cold persists after doing the above, take baby to see a paediatrician for evaluation.

.....are caused by viruses which will run their course with or without any medication.

Note that Most cold and cough both in children