Hello and welcome.

One thing I did when my kids were babies was I would turn on the hot water in the shower and steam up the bathroom. Then I would shut the door and sit with my baby in the steam for about 15 minutes at a time. I would do this two or three times a day. You can also keep a humidifier in his room (talk to your pediatrician or pharmacist about which ones are best. And use saline drops which are available in drug stores. Colds can be a serious thing with babies. My youngest developed a respiratory virus called RSV twice during her first year and had to be hospitalized both times because her lungs became very congested with phlegm and she was having breathing problems. It's rare, but it can happen. If your baby seems to have a lot of trouble breathing and trouble keeping down food/formula, take him to see the pediatrician asap. I hope you both will be feeling better soon.