help I'm a mess and need advice

Ok so my sons immune system has proven to be a slacking ass hole. He got his first cold at 3 weeks old and has gotten 3 more since then. He is currently one day 4 of a cold that's progressivly getting worse. I called the ER about the cold he had at 3 weeks which they wanted me to give a few doses of robatussin since he was having such a hard time breathing. well the last cold I broke and took him in and they told me there wasn't anything I could give him and I just had to wait it out. Well here we are again he has thick green snot, cough, green eye boogies, fussiness, sleeping more, I question if he has a sore throats but havnt gotten a good look. Idk if I should take him in to the clinic or just wait it out. He is miserable his nose is raw and bleeding and he acts like he feels like death :(