Boyfriend - cheating??

I met my boyfriend in Sept 2011 so we've been together a year and a half. We got into a routine fairly quick meeting up every second day and then spending the whole wknd together. So things developed fast and i fell for him pretty quick. Im 25 and he's 35.. In Jan, he was on facebook and i was looking in over his shoulder. Someone had sent him a private msg, he went to open it and i scanned through some of the names in his inbox. there was msgs to a girl from him asking when they could meet for a drink! We were in the sitting room with his parents so i couldnt say anything until we went to another room.. I asked him what he was playing at and he said he was messing with her, so i asked him what would he have said if the girl had said yes to the drink and he said he'd do nothin it was for the laugh.. I told him i wasnt comfortable with this coz it makes me look like an eejit.. so he said he wouldnt do it anymore. A couple of weeks later he was driving and asked me to log onto facebook on his fone so he could update his status (always been very secretive with password) so he told me his password and said he has nothing to hide from me. BIG MISTAKE! I logged on a couple of days later to see if he was still texting other girls, but as it turned out he wasnt. Then for some reason the other day i logged on again.. innocent msgs to a girl asking how she was, but since i didnt know the name i went back up the conversations and in July 2012 they were msging bout meeting for a drink etc but she said you're too far away coz they lived in different parts of the country so they left it there, nothing in the meantime.. Got me curious and mad so i went into the msg archive.. Msgs to one girl asking when they were going to meet up for a f**k but she knew he had a girlfriend so she said no. He deleted her as a friend. I then went back to when we first starting dating msgs to an ex saying he was going to call for a kiss, then in dec 2011 (together 4 months) msging another girl to meet up but from the msgs i gather she stood him up i even remember that date and know that he wasnt with me that evening but did collect me that night coz i was out for a friends bday.. they arranged to meet again but he stood her up, they exchanged numbers she told him she'd send me a topless pic if he send her something, msgs end in late decemeber 2011 with his saying he was deleting her off facebook coz she was a tease!!! not sure what came of that.. racking my brains trying to think back to the time and see if i remember anything but i cant!! We now are living together for the past month we are together constantly bar when i am working, he hasnt been texting any other girls since i asked him not too and there are no msgs on his fone. I am a total wreck i dont know what to think or what to feel!! I've never been this happy in all my life and actually hate thinkin of having a life with out him, i cant breathe properly and cant sleep for the past 3 days thinking bout it all!! PLEASE HELP or offer some advice, he tells me he loves me everyday we have a really good relationship always laughing talking, his family adore me and i have become close to his friends... i dont know if i should speak to him or try move on and start anew and give him the benefit of the doubt that he hasnt ever done anything on me just harmless flirting on facebook??

Perhaps, but why does he need to flirt when he has a girlfriend? It's about respecting the other person. If you wouldn't do this to him, and it makes you unhappy, then I'd say he's not really respecting you.