Can a bad tooth cause sinus problems?

Yes: It is not abnormal to have a patient come in with a toothache that turns out to be a sinus infection. Patients will describe pain in the upper teeth often not a specific tooth and pressure or aching and throbbing of their teeth. If the tooth is abscessed the infection can eat away the bone at the end of the root and provide a path to the sinus. Infection follows the path of least resistance.

Yes: If an upper molar has an infected nerve, it can drain into the sinus. Have a dentist xray the area you suspect the sinus is infected.