The liver points that I know of on the head area are between the eyebrows (those vertical lines indicate toxins/anger stored in the liver), the brown spots (liver spots) on face and hands, and a point on the surface of the tongue (tongue diagnoses) and lip diagnoses. That's all per Ayurvedic medicine, not Chinese Acupuncture.
I don't know of any points on the roof of the mouth whatsoever. I tend to think of any sore spots there as having to do with an abcessed tooth or sinus infection.
The main Chinese Acupuncture points for liver is right foot, between big toe and next toe, about an inch up on the foot, between ligaments. For gallbladder the top of the shoulders, both shoulders, that fleshy area that you can pinch, and the outside of the right thigh, mid thigh.