The part that concerns me is the title that includes "....but not a cheater" I would like to know what prompted you to say this? Because what defines a "cheater" is just that, someone that cheats or has cheated. Whether you want to or intend to continue to be one is up to you but you first have to get out of denial. Even though you have "admitted" to the mistake it seems as though you're deflecting taking the full responsibility of it. No one, even drunk is completely without choice unless they are passed out and cannot effectively make a choice (as in being taken advantage/raped). You still chose, albeit you were less inhibited to do so.

The scary part of all of this is... many times when someone is drunk they say they do things out of character but I say much of the time it brings out those things that exist in us that we hold inside when we are in control and more inhibited. Even though you have started on the right path, it's not going to be a short or easy one for you or your bf. He is going to have a hard time trusting you and I tell you the truth you CANNOT leave the burden of trusting you on him. It is up to you to go out of your way to accomodate and understand his fears. I cannot guarantee he'll ever get over it. But the only way is to understand, never do it again, and go out of your way to make yourself very transparent to him so he'll have every opportunity to trust you again.

On your part you need to do some soul searching. no one cheats for no reason. What drove you to even consider doing something like this when you say your bf loves you so much? Until you figure out why you would even do such a thing, you will not be able to get past it and change.

Hope this helps
~S4