My 4-month-old has been like this nearly from birth. He has a "flappy vocal chord" thing he'll outgrow. Lots of phlem too, that often causes him to "choke," and I pop up to make sure he's OK. Babies get colds and are fine, but yes, it's miserable for all involved.
I bought the Nose Frida (made in Sweden). It sounds odd, but it works. Much better than those bulbs from the hospital. You suck in air and a glob will come out of baby's nose. Then he smiled at me. So, that's the route we've taken. First spray saline, then use the Nose Frida. Hope he feels better!