Have you been tested for any food allergies? It could explain (partially) why you feel ill after eating unhealthily. For some people, the cause of their mucus/post nasal drip is GERD or acid reflux.
I've always had constant post nasal drip. But,unlike you, I can't clear my nose as easily. I've thus developed a habit of sniffling into my head (gross, I know).
Yet I, too, often cough up mucus after eating, and in general. I've tried asking my ENT why I can't blow my nose, and he had no idea. Have you seen an ENT? Maybe it's an underlying condition and the sickness from eating is just a symptom of that. Sounds like it might be, since you get sick from eating a lot and have a ton of post nasal drip.
As far as symptoms go, a neti-pot may help, and maybe flonase. I need to use mine more. You will have to blow your nose after using it (to get the water out of your nostrils, but it can help people with allergies and general congestion clear up their sinuses).
Have you been tested for environmental allergies or even Candida? These can cause the issues you are having. Allergies are the pits to pin down, but the time it takes to do the tests are well worth it.
Increased mucus might be due to increased inflammation.
Have you tried a drug to decrease gastric acid production?
I hope you find relief soon!