How do I fix this complicated situation?

I'm a newlywed (Nov. 2013), but am having a difficult time with my wife, and a few misadventures on Facebook where she seems to attract other men, and I basically find out for myself the hard way with regards to her chatting and telling white lies. We met online in Jan. 2013, and began a LDR shortly afterwards, because she relocated to the East Coast while awaiting my relocation and job transfer from CA.

The way I found out about her texting and messaging other men was through her old cell phone, where I found FB chats with other men. Some were harmless, but a few were just plain hurtful and my heart sank when I read them. She lied about her marital status, saying she was still single, she used terms of endearment such as "honey", "dear" with some of them, and when going through her FB photo albums, I looked through some of the men I was suspicious of, and saw a few replies on their feeds where she appreciated "this" or "that" and was getting friendly with them. Also, I saw through her photo album some of those men "liking" pictures I took of her, as well as saying crude things.

This evening, I saw she "liked" and "shared" a link on FB to a personals site where "you can find a honest man to match up with"... I immediately shared that link back to her home page on FB and asked her what that was all about... A married woman liking that type of website... She has a 5 day a week live in nanny job across the river from me in NYC, and we don't see each other till the weekend. I hope it's boredom since I'm not by her side, but when we see each other, there's no texting or phone calls to or from weird men since she doesn't hide the phone screen (Galaxy 5) when she uses it. All contact from her is to friends and family we both know well.

I'm at my wits end, but have confronted her about the infidelity (yes, I told her she was cheating...) by her contacting and chatting with strange men on FB... I told her I invested much in our marriage, and by her doing that, she's destroying whatever we're building... I put my foot down and told her she needs to focus on the relationship and not strange men who don't give a crap about us... Only trying to get into her pants, is all... She apologized, and said that she's at fault since she's not computer savvy, and got caught up in a type of FB addiction, but I told her everything she was doing to me by her actions...

I am not a weak person, am an Alpha male, never ignores her, always gives her attention, always listens to everything she says and never neglects her. I just hope the pattern is broken, and that's the last of her "curiousity"... Thanks for listening!