It's when you have a
heated argument with another person, and he/she keeps telling you '
oh my God', by implying that they don't want to hear you speak, is when you use the Don't "
Oh My God" me, which means you are right, and the person should listen whether he/she likes it or not.
Jennifer: Stop talking and listen to me. He is mine, and you should leave him alone.
Candy: Oh my God, when will you shut up about this?
Jennifer: Don't "Oh My God" me.... you know I'm right about this. He loves me, not you.