I think a lot depends on how her current relationship is going. If she's happy with him, you've got a snowflake's chance in hell. But if she's single or miserable, there may be *little* more hope.
If you do get her back, all this effort will be wasted if what went wrong in the relationship hasn't been fixed. What have you done to change yourself so that these fights won't happen? Of course, if you want to have her back, you must accept her for who she is and change yourself to be the man she needs you to be. You can't ask someone to come back and then ask them to compromise.
And of course, seeing someone else after you will have given her more life experience and therefore changed her.....don't expect her to be exactly the same girl you dated earlier.
Never regret anything that has happened in your life. It cannot be changed, forgotten or undone. So, take it as a lesson learned and move on.