It could be from the rhinitis. Nasal drainage can cause nausea - https://www.medicalnewstoday.com/articles/319636.php
It could also be a gallbladder issue - https://www.webmd.com/digestive-disorders/what-is-chloecystitis#1
There's also uvulitis - https://www.healthline.com/health/swollen-uvula
It could be a lot of things, but for sure, you need to see your doctor about this. At the very least, it sounds like you need something more than cough syrup to treat the rhinitis.
Let us know what happens, and feel better. :)
Ya, it could be the whole issue of having been sick. When I have a sore throat or am sick, I can get gaggy too. I throw up so easily and eating can trigger it if it's already agitated there already if that makes sense. I'm always down for losing a couple of pounds so try to look at it as a benefit to being sick. ha. But know that probably isn't the best way to look at it. The most important thing to do is to stay hydrated. This is important when sick with rhinitis or a cough because it helps thin mucus so it doesn't get caught up and start festering into a secondary infection. We can go a pretty long time without eating but need hydration to live.
Let us know how you are doing!
Hello~I would suggest seeing your doctor, it may be due to a residual infection from you being sick, or it may be something like food allergies. In any event, you don't want to stay like this every time you eat. The doctor will probably run some tests and after he/she gets the results, may be able to give you some medication that will help.