Is it possible to trust your partner again after they have cheated?

[z2010]

My boyfriend cheated on me last year around August . We have been dating for almost two years now . He didn't necessarily do anything but he had been texting a girl he went to hs with behind my back . I looked through his phone which is how I found out . He told her he loved her .... And we live together :/ His reason is that he just wasn't happy at the time .. Ever since then I don't trust him at all. I constantly feel like I have to look through his phone or whenever he's on his phone he's texting her or something . I love him .. we planned on getting married and such but I honestly can't keep living my life having to wonder what he is doing behind my back . It hurts so much . I know it happened a while ago but I can't let it go ...and the girl he cheated with me on . I feel like she knows I don't like her so she constantly does things to piss me off like follow him on Instagram and twitter and add him on Facebook. I know I might sound childish and I am in my 20s but I can't help it .. I want to trust him again but a lot of people say without trust there's really nothing .. Any advice for people who have been through this ?
They were friends with benefits back in the day... And back in the day he was a player and she wanted to be with him but now I Think he regrets not being with her back then because the texts said if I could go back in time and change things I would in a heartbeat .. I love you... That's how he said it . I check his phone because Ive caught them talking before but it was when we fought and broke up. I just had a feeling ... That is why I checked .