What Could Cause Persistent Itching In My Left Sinus And Upper Mouth If Allergy Medicine Isn’t Helping?

The sinus on the left side of my face has been severely itchy and causing the farther back, top of my mouth to itch. I assumed it was allergies but allergy medicine is not improving my condition. I wonder if something my be stuck in my sinuses, like pet hair. I blow my nose and nothing comes out. Any recommendations?