Can I forgive my husband? Should I? He said he cheated but now says he didn't! How can I find out the truth?

We have been together now for 3 1/2 years and married for 4 months, but about 8 months ago we got into a huge fight over something stupid and he left me. He went to his mothers for a while and then moved in with a girl from his work. When we started talking again he told me that he was haing sex with her and that he didn't want to be with me any more and that he loved her. A few weeks later we began to spend time together again because I wanted him back so he said he'd give me another chance. He would come home for a few days at a time, and then leave to go see her saying that his feelings for me weren't changing. He lied to me about seeing her and still telling her that he loved her multiple times. This entire time I was crying ang begging for him to take me back.
Four months after he left, he decided that he wanted to get back together and he told me that he lied about sleeping with her and only said those things because she told him to and because he was confused and upset. She told me as well that they were not (after originally telling me they did it all the time). He told me he had NO physical contact with her whatsoever, until she emailed him a picture of them kissing and I found it. He says he forgot because he only did it on a dare. But he still swears up and down that he didn't have sex with her.
I thought getting married would change things but now I am even more confused. I don't know whether or not I can believe him and I don't think I can trust him again because of how he hurt me and how he lied about it. We're both young and I don't want to be stuck in a marriage where I am not happy. What should I do?