Gum pain in the back of my mouth, behind the last tooth.., what to do?

Few reasons: The most plausible cause is periodontal abscess infection. If ur wisdom tooth is partially erupted as ur last tooth , then it is called pericoronitis and it is more of a gingival abscess. In either case, see your dentist. He/she might even refer you to a periodontist.

Wisdom tooth: Likely inflamed wisdom tooth. At your age, for best results with wisdom teeth, make sure you are evaluated and treated by a board certified oral & maxillofacial surgeon.