My left upper back molar and gum around it hurts... today they found left maxillary sinus chronically inflamed... is it normal to have pain there?

Yes: Sinusitis can definitely cause maxillary tooth pain. When the sinusitis clears up, the tooth pain should as well. If not, see your dentist.

DDS/ENT check: See your dentist, usually sinusitis can result in pain upon biting for maxillary molars. Just to make sure that everything is ok dentally, go get it checked out.

Very common: also called a dental sinus. Very common when the roots of the upper molar teeth are in close proximity with the sinus area. Removing the dental infection is the only successful treatment for a dental sinus. See your dentist for consultation and treatment.