Sorry in advance for the thoroughly religious nature of this post :PI've always taken wrongdoing very seriously, and in many ways, not as seriously as I should. Everyone, from my GF to my friends, even my counsellor, says I hold on too closely to the things i've done wrong. In some ways, I still don't agree, but I came upon a passage that really convicted me, especially regarding the cheating, from Hosea 2:
"I will punish her for the days of the Baals to which she burned incense. She decked herself with her earrings and jewelry, and went after her lovers; But Me she forgot,” says the Lord. “Therefore, behold, I will allure her, will bring her into the wilderness, and speak comfort to her...“And it shall be, in that day,” says the Lord, “That you will call Me ‘My Husband,’ and no longer call Me ‘My Master,’ For I will take from her mouth the names of the Baals, and they shall be remembered by their name no more. In that day I will make a covenant for them... I will betroth you to Me forever; Yes, I will betroth you to Me in righteousness and justice, in lovingkindness and mercy; I will betroth you to Me in faithfulness, and you shall know the Lord...Then I will sow her for Myself in the earth, aAnd I will have mercy on her who had not obtained mercy; Then I will say to those who were not My people, ‘You are My people!’ And they shall say, ‘You are my God!’”
I've found a lot of power and beauty in those words. Hosea was a prophet whom the Lord told to marry a whore, that God might use their marriage as an analogy for His relationship with Israel. God spoke the above to Hosea before the many, many judgements that God pronounced on Israel, He knew that He loved them, and wanted nothing more than to bring them back. Hosea loved his wife, and despite her adulteries, he saved her and brought her back to him. Throughout Hosea, God pronounces judgement, but again and again, He begs Israel to repent, that he might not be angry with them. 
I struggle with that. I want to do something more than just say that I'm sorry. I feel the weight of what I've done, both against God and against my GF, and I know that nothing I can ever do or say is going to make up for it. But there comes a time when I just have to sit back and accept the mercy that I've been given, both from God and from my GF.
I talked to my GF last night, and she told me how much she loved me, how much she loves how much our relationship, and how much it has grown because of all the effort I've been making to make it better. You'd think that'd make me feel better, but it didn't. It just made me feel worse. Everything I do in my relationship, recently, makes me just feel the weight of what I did to my GF. I'm happy that our relationship still exists. I am happy beyond all belief that my girlfriend has forgiven me, and I can even see a future for us, and am planning for that future. But my doubt and my fear stands crouching, always, waiting to jump whenever I think too hard about our relationship. 
Acceptance is hard. I may be able to intellectually accept it, but emotionally and spiritually? That's going to take time. 
One day. 
-N2G