My son got a cold around 3 months or so, just keep him hydrated and listen for his cough. If it gets really bad, take him in. Also watch his temperature just in case. But when babies have colds there isn’t really anything we can do or give them, just make sure he is comfortable.
And above all else, don’t be afraid to call his pedi if you are concerned and see what they say.

Humidifier and saline spray poor guy hope he feels better