Will a tooth infection kill me?

Not all the time: Most tooth infections are self limited. There are cases still, where the infection spreads in the blood stream causing sepsis, infection invades important blood vessels leading to the brain that indirectly can cause death. If you have a suspicion for a tooth infection see a dentist asap.

It potentially can: Unless treated properly and quickly.

It can: It can spread bacteria to the heart and cause the valves to malfunction. One scary case i had started as a tooth abscess. It progressed to such an infection that the airway was almost completely obstructed. The patient needed a difficult awake tracheostomy placed. Plus tooth abscess hurts a lot. Best see a dentist.