Years ago I read a short story in a magazine-- I'm fairly sure that
the title of the story was "Make Me." It was first-person, told by a
male teacher in love with a female student, and the teacher's
ex-girlfriend, also a teacher, who is having an affair with a student
of hers (incidentally, the female student's boyfriend.) I'd love to
know who wrote the story, and where I can find it.

I suggest going to a library where they can do searches within
magazines.  They may request you to give a list of possible magazines
to try.  In fact, if you have a few magazines in mind, you may be able
to do this search online at the magazine's website (or maybe a
library's website).