I've been cheated on, and I've cheated.
When I cheated, it was because I fell desperately in love with someone else, and felt trapped in my life with my existing partner (we shared a home, worked in the same place, shared our friends, he'd left his home town to be with me, and I loved him dearly for a long time, but in the end I just felt trapped (I was very young)). And the person I cheated with felt like my soulmate, like nothing in the world could possibly compare to him.
I do understand that sometimes affairs aren't about getting one over on someone else, or having your cake and eating it, sometimes it's just a shitty thing that a, usually reasonable, person does.
I've also lost my best friend (unrelated), after 15 years of being like sisters, we haven't spoken for eight years. And it still hurts.
I can really empathise with how you're feeling. But you only really have one choice now, which is to put in your big girl pants, accept that you made a mess of things, and move on.
This doesn't make you a bad person, it makes you a person who has made some shitty decisions.
And yes, it's unjust that you bear all the blame, and you are the only one being punished. But that's just how it goes, grab big girl pants and move on.