My girlfriend is lying to me and acting shady but I don't want to break up with her, what should I do?

So the other night my girlfriend's (we've been dating for 9 months and are very serious) cell phone vibrated that she got a new text. My gf was downstairs and the phone was behind my head on a pillow so I checked it out of curiosity to see who it was. So yeah I know I shouldn't have invaded her privacy by looking through her phone but at the time I really didnt think anything of it. But the text was from someone who showed up as ';satan';. The text was really dubious and because I had just found out the other day that she had been talking this guy ';innocently'; behind my back on facebook I was suspicious and decided to look through her inbox. Again I know I shouldnt have invaded her privacy but lately I feel justified in being suspicious. So I looked at her incoming messages from this ';Satan'; and they were all really suspicious. Like one message said ';oh you just like torturing me don't you?'; and another message said ';why don't you put your money where your mouth is and get down here'; her outgoing messages were deleted but it was obvious that they had been conversing through text. So when my gf came upstairs I told her she got a text from someone going by Satan and asked who it was. (I asked very calmly and nonchalantly too) but she immediately got very upset and defensive and accused me of invading her privacy and not trusting her. So I got angry too and kept asking why she couldn't tell me who this person was. And she kept swearing that she had no idea who it was. That some random person had just sent her really weird texts like 6 times and that she had no idea who it was.....sounded like bullshit to me. But she swore on her life she didnt know who it was. Still I called her a liar and yelled at her for lying right to my face like Im some kind of idiot and am supposed to believe that some random person she doesnt know would text her a good 6 or so times in cryptic messages that obviously implied she was talking to this person. I got really upset and tried to walk out...I know I should have broken up with her and that she is most likely lying to me...but I just couldnt, I wasnt strong enough...I dont want to live without her..so this morning we talked again after I had slept on the couch that night (didnt actually get any sleep as I kept thinking I should walk out the door and never come back). Again she swears on her life that she would never lie to me and that she has never lied to me before so why should i not believe her now. Then she made herself out to be the victim and said that I clearly dont trust her (which truthfully I dont know how i can trust what she's saying to me). She swears that she would never cheat on me... and even through the bullshit I am very confident that she wouldnt cheat on me and that she hasn't...yet but what am I supposed to do now? She is clearly lying to me, which means she's hiding something from me, and the whole thing is so ****** up. For the moment I told her that I love her more than anything and that I dont want to be without her so If she's saying that she doesnt know who this satan person is then I'll believe her and trust her....and thats how we left it..........what the hell do I do now? I don't feel ok knowing she's most likely lying to me...and even though she says she wants to spend the rest of her life w/me etc. etc. I have to wonder...My girlfriend is lying to me and acting shady but I don't want to break up with her, what should I do?
If you think she's lying, she probably is. And, even if she isn't...the trust seems to already be broken and you'll always second guess whether she's lying or not in the future. It's not worth it..