Could pain in the ear and the teeth be caused by a headache?

Yes and the reverse: Because of the innervation of that part of the facial skeleton, pain in the teeth, ear and head can be associated and initaited be a disorder in any of them.

Also...: An infected tooth is often asymptomatic (without symptoms) for years. That can change overnight. The first symptoms often reported by patients when the infection from a tooth begins to spread is ear pain and headache.