How can I trust her again?

Anonymous
My girlfriend and I have been seeing each other for almost a year but have been good friends for more than 3 years. Most of it was stupid problems that popped up due to my insecurities after having her moan her ex's name in her sleep. They were together for two years in which time he cheated on her (Not sure if she's over him)
One night just before V-day she moaned his name in her sleep and it bothered me but i ignored it and then i started noticing things. I saw that there was still an old anniversary card on her shelf one night and there is a picture of them with friends on her wall.
After two months of suspicion and worrying she finally dragged it out of me. It was a big fight and she told me it was just cause she hasn't spring cleaned and she didn't even know the things were there, she also told me she was suspicious of me cheating (which by the way i have never done nor plan to do... i do truly love her and have never felt this about someone). The fight dragged on for a few days and things were starting to get better. We both promised to tell each other the truth ad tell each other everything the other person should know
A few weeks later i remembered seeing her with another guy less then a week before we became sort of official and asked her about it. At first she told me she couldn't remember it, then she told me it was just a friend and that there were other people around. Each time I had to find holes in her story and i had to catch her lying before she told me the truth.
It was a big fight leading to us almost breaking up. She then told me a bunch of things she has kept from me... I just don't know if I can ever trust her again or if she is actually telling the truth. I don't want to be the boyfriend that doesn't trust his girlfriend. (she offered for me to go through her phone but I don't want to be that guy who needs to do that... i have been tempted cause she seems very protective over it, but I've never done it behind her back). Any thoughts on the situation?
How can I trust her again?
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