my girlfriend is convinced i am cheating on her

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My girlfriend thinks i am cheating on her?

well it started off few months ago when this new friend came into the picture. she is fun, so we hung out(mostly with other people, never go out by ourselves). one day when i introduced both of them, my girlfriend suddonly got very defensive and told me to stay away from her. she said that she is trying to lure me or seduce me etc. anyways, now since we have mutual friends, we still hangout(i can't telll her to go away and be rude for no reason). i started lying to her. whenever she would ask me who i am hanging out, i'd say everybody's name but her to avoid argument or conflict. i wish things would've stopped there but one night everything just got worst. i was suppose to go play pool with my buddy and he got off work late. my friend meanwhile called me to hangout so i told my buddy that i'll wait for him at the bar. at the bar there were quiet few girls that i knew(including that girl) and not that many guys. i kept drinking cuz my buddy was driving and two things happened. i got pretty drunk, and my buddy got stuck at work. meanwhile, my girlfriend told me is having a girls nigth out with her friend. my buddy got there pretty late, so i told him to drop me off at my friends house few blocks away so i could pass out there, sober up and drive my car back as i needed it next day. i came to my friends place and sat on the sofa and passed out. my phone was on silent when things couldn't go any worse. i woke up 7:00 am and saw like 20-30 missed calls from my gf. so i get up and told that i was with my buddy playing pool to avoid further annoying questions. next day she see pictures of me on facebook that someone took of us that i don't remember and that girl my gf is insecure from is noticeably close to me. now i am in trouble. she is very convinced that i have slept with someone if not her. thats why i didnt pick up her phone. plus she caught me in lie so that is another evidence for her to suspect me. now i don't have any reason to cheat on her as i love her and want to settle down with her. we have been together for over two n half years.
just wanted to add, that in the past i have had suspicions on her that she is doing something behind my back but never got anything solid. e.g. passed out drunk with her ex who is now her friend, staying at this guys place telling me there are other people too till 7:00am getting drunk and high. that was in the begining 5-6 months and then everything just went away
now my biggest fear is that she might go out and cheat on me thinking ive done something, especially when i had suspicions on her in the begining of the relationship. any help would be appreciated. thanks