If the relationship lasted only a few months, I'm surprised you are still hung up on her. If she asked you not to contact her when you tried to apologize, then I don't think there is anything you can do. Maybe the reason you are not being able to move on is because her cousin reminds you of her too much and you feel guilty about dating the cousin. You shouldn't feel guilty about dating her cousin. Once you break up, it's none of your ex's business who you date. I don't think you owe her any explanation. I'd say try harder to move on and don't let your past relationship affect the current one negatively.