Lie and Betrayal

I am lying to my ex girlfriend. Just before we broke up I kissed another woman. I thought the break up would clear my conscience and dissolve my wrong, but it hasn't and now I don't know how to tell her, for fear of her hatred.
It is in the way of the possibility of us getting back together. Because I can't admit it, I have to let her go.
It eats me up inside and I can't sleep properly.
I hate myself for the act but also for the shame of not being strong enough to admit the mistake. I can't bear the thought of her not forgiving me.