Newborn has a cold?

What can I do for my newborn if he has a cold? He's not running a fever and he's eating perfectly fine, so his doctor isn't concerned. Is there anything I can do to help? So far I'm just using the bulb syringe on his nose to clear it, but he's coughing and still sounds a bit congested. 😔 I also put baby vapor rub on my chest so that when I hold him, it helps clear his congestion, but I'm not putting it directly on him.