Well I am a recovering alcoholic and addict so was and active member of AA for many years so I have to say that the steps are what helped me the most. The same principles can apply to anyone though.
First of all you admit the exact nature of your wrongs to someone. You already did that.
Finding away to make ammends is more complicated. For one thing you stopped the password facebook scenerio. That is good. Talking to others helps. You are not alone. To me what you did is not a big deal. I know that to you you feel alot of shame about it. That is valid. Learning to forgive yourself is a process not an event. Look in the mirror right in your own eyes and say "I love you and I forgive you." Do this over and over. That is one technique. Every time the thought intrudes your head say I forgive you. Sounds like you have some OCD stuff going on over it maybe. I don't know your history.
Journaling is another technique. Write it all out the whole relatiionship and what you are ashamed of and then burn it. Burning it is very symbolic of letting it go.