I would call his pediatrician just to let them know what's up, but he should be ok. My daughter caught a cold when she was 3 weeks old as well. I called her pediatrician, I didn't have to bring her in, I just let her know what was up and she told me to keep an eye out for fever and to try to keep her comfortable and hydrated, which just meant nurse nurse nurse. I did use breastmilk in her nose to try to break up the snot, and then I sucked it out. Worked way better than saline for us!
Your pediatrician may want to see him, he may not, but I would still call just to be safe. I'm a worry wart though.