Hello, KDD . . . it has been my personal experience that sinus pressure causes pain in upper teeth, and ear and tonsil pressure causes pain in lower teeth, especially molars. The reverse can be true, also. If you have cavities and/or abscesses, the pain can go to the sinuses, ears and tonsils.
I have found that after three or four days on antibiotics for sinus infection, the pain in the teeth usually goes away. If you still have problems when your antibiotics are done, you should let your doctor know.
Best of luck and let us know how it goes!