Painful, swollen gums in very back of mouth. face slightly swollen. what could this be?

Wisdom teeth: At your age i would suspect an infection around erupting wisdom teeth if you have not already had them removed. Very common, it is called pericornitis, and can be treated by a general dentist with cleaning, irrigation, and antibiotics. Because there is often not enough room for the wisdom teeth to erupt straight they come in crooked, allowing debris to be trapped under the gums. See a dentist.