Can a severe cavity make your face swell?

Yes. If a cavity is left long enough that the inflammation passes the root tip and spreads into the surrounding tissue, the face can swell. Swelling of the cheek or jaw with fever, tender lymph nodes under the jaw, and difficulty opening the mouth are signs of an acute infection (a dental abscess). At this stage painkillers alone will not resolve it: antibiotic treatment is needed along with drainage of the pus and either root canal treatment or extraction of the tooth responsible. However, if the swelling spreads toward the eye or the neck, or breathing or swallowing becomes difficult, it is an emergency - go to hospital immediately.