How do I relieve facial pain from a possible sinus?

ENT or Oral Surgeon. See ENT doc. If no diagnosis or dental problem. See oral surgeon. If TMJ, see TMJ expert.
Facial acupressure. Self care is powerful! use all points around the nose. If you have jaw issues, do those muscles too. Just fine a TMJ chart on the web.
What is the cause? Is the sinus problem caused by an infection, tooth decay, trauma, cyst formation, cancer, etc. Without a proper diagnosis, it is difficult to determine the treatment. Many different antibiotics, antihistamines, anti-inflammatories, or narcotics could be used. Or simple moist, warm compresses to the cheek or sinus rinses may reduce the pain.
Decongestants. Other helpful remedies are saline nasal spray, drinking warm liquids such as soups. A humidifier may help, warm compresses may help.Drink plenty of liquids and finally, if antibiotics are ordered finish them.