I used to have that problem for years, but I knew what caused it, it was phlegm. And I knew what was causing the excess phlegm, I just didn't want to stop smoking, even though the "scratch test" I took when I was a kid showed I was allergic to it.
Phlegm drains down the back of your sinuses and into your stomach, and through your digestive tract, at a slow but steady rate, pretty much constantly. But during the night you're not eating, and you're laying down, so the phlegm can pool in your stomach, then you wake up and eat or drink something, and you've got an oil slick of goo sitting on top making your stomach upset and the result is nausea.
In my case I figured out that I could chug a bunch of ice cold water first thing and then throw up water and a few tablespoons of bile and phlegm. Then I would immediately start feeling tons better, and the cold water made it less unpleasant than either feeling nauseous for a couple hours or throwing up food. Or I could just out-wait the nausea, and then the phlegm would eventually pass into my guts, but I preferred twenty seconds of yakking cold water to an hour or more of feeling queasy after eating or drinking.
I eventually solved my problem by stopping the intake of allergens into my system, namely cigarette smoke, which I was both allergic to and addicted to (because I'm an idiot). With less allergens came less phlegm, no morning puking.
Your problem could be completely unrelated but I thought I'd throw that out there because the symptoms are the same.
If your problem is similar to mine, perhaps there's more dust in the air, or animal dander, or some other airborne allergen that is causing more phlegm production?