She will be very stressed out ecause of her overbearing parents… this in turn will probably make her overreact and get extra emotional at times.
You fucked up by lying. That is the big problem. “You just gotta say I did it because I didnt want you to hate me… but I fucked up. It was a mistake.”
You need to learn that sometimes its better to ride a situation out and do nothing rather then try everything. If the relationship was as good as you say then its not done. You HAVE TO give her time to calm down. Her dumb parents are up her ass right now so it will take even longer for her to relax to the point where she is thinking rationally.
Just wait. You will be fine. Skip the gay doom and gloom shit. Be optimistic and have confidence in yourself, her, and the relationship.
edit: a night with the boys is not the best idea. If she sees you out in the bar and club scene RIGHT AFTER you broke up then guess how thats going to look? Yep… you dont give a shit about her and are out looking for new ass… that will not help her calm down and get over your insignificant mistake.