A sinus infection can cause tooth pain.
More Info: Sinusitis may be a cause of dental pain, in the same way that dental pain is a symptom of sinus infection.
What Is a Sinus Toothache?
A sinus toothache is dental pain caused by a sinus infection. This pain around the teeth is the result of the infection of the top sinuses, wherein the sinuses filled with fluid cause pressure on the area just above the back teeth, thus causing them to feel pain. It may also cause sensitivity in the upper back teeth are that can be experienced when chewing or applying pressure on the said area of the teeth. 
Conversely, sinus infections can also result from dental sources, particularly an infection in the maxillary back teeth roots, which are located in the sinus cavity. Studies show that ten percent of all sinus infections are caused by a dental source. 
What Is A Sinus Infection or Sinusitis?
A sinus infection, also known as sinusitis, commonly refers to an acute bacterial infection of the sinus cavities. When sinus infections are caused by bacterial infection, this leads to the collection of mucus in the sinuses, which become inflamed and congested. Bacterial sinus infections last for at least ten days.  Sinus infections can also be caused by allergies, chemical irritations, mechanical obstructions, or an infection in the maxillary tooth. 
The Location of the Infected Sinus Determines the Symptoms
There are four cavities known as paranasal sinuses that can become infected to cause sinusitis. They all share a few common symptoms, but often the pain associated with the infection is limited to the location of the infected sinuses. For example, an infection in the frontal sinus will cause pain in the forehead where the sinus is located. An infection of the ethmoid will often cause pain around the eyes. The pain associated with the sphenoid sinuses could involve your neck and earaches. In the case of tooth pain, the sinus infection is likely to be in the maxillary sinus, which is located in the cheekbone. 
How to Determine if Sinus Infection is Cause of Tooth Pain
A sinus infection is not the only reason for dental pain, therefore it is important for doctors to assess the history of the patient regarding sinus infections, perform exams on the dental bone to determine the source of the pain, and actually treat the sinus infection to either rule it out or conclude that it is the cause of the said tooth pain.