Dude, act LIKE A MAN! Dump her once and for all!
That´s not because of FB. She has the right to have her Facebook (as long she doesn´t harm the relationship being there all the time, giving little or no time to you).
I´m sorry to tell you this, but it seems to me (from what I read) that the problem of you relationship it´s YOU. She only does what YOU allow her to do. When a chick cheats on a guy, that means only one thing: kick girl´s ASS and move away!!!
Besides, she´s the dominant part of the relationship, and we also know what that means. When a guy shows himself insecure and behaves with all the things that comes from that, the chances of being cheated increase a lot. As simple as that. So, do what you got to do to improve yourself on that department.
Bro, make youself a big favor and dump her right away! Dude, there are too many women out there. Dump her! Period.