My baby is 8 days old and has had a dry cough for the past 24 hours, he has been bringing up quite a lot of his milk and tonight he started coughing up a lot of thick, bubbly mucus and wouldn't stop coughing up this thick mucus for about 10 mins or so.. then he brought up this bright yellow vomit, I'm not sure if it's reflux or what's wrong but his coughing fit really worried me as he looked really red and struggling for breath. Has anyone else experienced this? He has been checked out and his pulse, temperature and everything is fine. Anything to help stop these coughing episodes happening?

Thanks in advance (concerned first time mum) xx