Break up with her. She had an entire month to weigh her options and chose to hide it from you. She doesn't care about you, and is probably only in it because she feels like she has to be with somebody in order to be happy. I could understand letting her off if it was just a one time thing, but an entire month? She doesn't deserve the respect you're giving her.
You gotta love what's good for you, and obviously she isn't good for you.