Please note that I am not trained in singing. There are certain muscles in the throat that allow you to close off your mouth and nose independently of each other. When I sing loudly (which is the only way I can sing reasonably in tune), I find that I tend to close off my nose using said muscles, and then I get nauseous. However, if I make a conscious effort to keep it open, I don’t get nauseous. Is there a direct link between nausea and singing through a closed nose?
There's an old joke; "Doc, it hurts whenever I do this."
Doctor says, "Don't do this. That'll be fifty dollars."
I don't clearly understand the palate/sinus phenomenon that you are describing, but if you can sing nicely in tune while training yourself to consciously 'keep it open', then continue to train that way, and everything will be fine.
Many singers have to train certain disciplines that may seem counter-intuitive at first, but later on become instinct.
Keep on working on it, and good luck!!