A common cause of a sore tooth and sore throat is the simultaneous inflammation of the wisdom teeth and tonsils, i.e. pericoronitis and tonsillitis. But the two are not necessarily linked, it’s just that the body’s own resistance has dropped, which leads to two different inflammatory conditions.
The other thing is that toothache can cause inflammation of the tissues around the tooth and can also cause laryngitis or swollen lymph nodes leading to a sore throat and pain in the face or neck, and can even cause difficulty in opening the mouth and affect swallowing.