Why do you need to let it go? Why is forgiving yourself important to you?
Betraying someone you love just isn't, in my opinion, something that we "forgive". At least, not in the sense that it will one day, "be okay" or something that we can look back and laugh about. Just for the sake of comparison, I lost my father to heart disease when I was 16. My father was dead when I was 16. And when I was 24. And 37. And 44. And 56. At no point in those 40 years did I ever "get over" his death, nor will it ever okay that he's gone. That loss is permanent. I cannot get back the time with him that I so dearly wish I had to spend together. Some things never resolve for us in a way that is convenient and comfortable.
What helped me the most, ultimately, was to reframe what it was I wanted to accomplish. It wasn't that I wanted to be forgiven. What I did is not something that's forgivable, at least not to me. But what I CAN do is allow myself the grace to view my life and my worth from a larger perspective. The affair does not define me as a person. Rather, I see it as a point in time, a part of the story of my life which is still ongoing.
The very best books and stories have a climax of some sort, a point at which something bad is happening or about to happen, and it is at that very point that each of us clings to something solid, sits up in our chair, and wait with bated breath to see what happens next. And in every book, the story goes on, and the problem gets resolved, one way or another. Here's the thing however, the book or story isn't about the climax, it's about how it resolves.
It's exciting to watch as Ebeneezer Scrooge, the stodgy, miserly banker with a heart of stone, is forced to face himself and his true nature by the ghosts that visit him. But the part that we really remember, the part that touches our hearts, is when he learns his lesson, when he accepts joy and love into his heart, and when he changes for the better. At the start of the story, we can't stand Ebeneezer, he's everything we loathe in a person. By the end of the story, he is our hero, and even the hero of the family whose father he mistreated at work for so long. The real lesson here is that we are ALL redeemable in some way. It will never be okay that Ebeneezer was such a jerk for so many years. That part of his life is frozen in time. But people love him all the same, and they do not define him by his faults, but by how he overcame those faults, and became a better person instead.
THAT is how you move forward, and THAT is how you learn to live with yourself. You do so by being someone better. You do so by not defining yourself by your faults and poor choices, but rather, in how you overcome those faults, and how you make better choices moving forward. You don't forgive what you did wrong, rather, you offset your faults by being an even better person than you were a lousy person, if that makes sense.
Be honest. Be truthful. Be dedicated and authentic and humble. Be brave and understanding and assuring of others. Be empathetic and calm and reasonable. Be the kind of person you admire most in the world. Be the kind of person that allows you to sleep peacefully at night, knowing that you've done your very best every day.
As a special added benefit, when we do this, we not only teach ourselves how to overcome the challenges in our own lives, but we also teach those skills to our kids by modeling for them how an adult responds to the things they've done wrong. If it was your child that did something wrong, you would not want them to crawl under a rock and hate themselves forever. You'd want them to focus on what wonderful people they really are inside, and who they can be. So you do the same. You show them that an adult OWNS their mistakes and poor choices, does all they can to make things right, and then takes steps to be a better person so that they will never make those poor choices again. That's a super important lesson to teach our kids. Parents aren't perfect. But we can authentic and decent and responsible for our own lives.
Good luck to you.