Sick baby :(

Im a first time mom and my son is 3.5 weeks old. He has been sick for the last 5 days. I feel like a giant panic attack. he doesn't have a fever just really congested, coughing, sneezing, and has thick green snot. when he lays flat he breaths really heavy and starts wheezing so I have been having him sleep in one of his portable rocker thing so he is slightly inclined. I have called the doctor a few times and sent him a video of his breathing so taking him in at this point wouldn't do much. I sat up watching him sleep until 3am before I finally dozed off last night. I feel helpless there isn't much they can do for a cold and I feel like he is so fragile. They have me saline flushing his nose and giving robatussin. To top it off The doctor said it sounds like I have influenza but waited to long to treat it (I was given Tamiflu in the hospital because we got exposed to influenza so I think it's why my symptoms were tolerable at first) I feel like I'm running on fumes I just want my little guy to be okay. Has anyone had a baby this young sick what do you do to make it through 😢