How do you find peace after an argument with someone?

[Anna]

Think about it. You "met" her on Facebook. You don't really know her in real life, and she doesn't know you. She is no more real to you than I am; I'm just a screen name and an avatar. Why allow what she thinks to disturb your heart? Particularly if you know it's not true.

If you find yourself obsessing about such an unimportant person, perhaps you have issues with a need to control others. Perhaps your distress is because this unattractive controlling trait has been revealed, brought to your attention so that you can't ignore it. Maybe it's time you worked through your issues. When we release the need to control others, the need for constant applause, acceptance and approval of everyone we come in contact with, our lives become much more peaceful.

ETA: You said "there is this girl on Facebook." That didn't give the impression you knew her IRL. If you know her IRL you could confront her in person or on the phone. But you can't control others' responses to you which are based on their opinions, just as they can't control you. The issue is your need to control others. Deal with that and you'll find peace.