I had a similar experience during a three-week cold, but in my case once I started vomiting I kept vomiting up slime until two days later I got some medication to calm my stomach. Had a mild scare because of chest pain right after, but it turned out to be an inflamed ribcage from all the coughing and vomiting.

I finally realised I kept having recurring colds because I had silent acid reflux, without any symptoms of acid reflux. After 8 months of getting sick every 2 months and staying sick for weeks every time, I started a diet against reflux and so far I have not been sick yet (4.5 months later).