There is nothing wrong when you long to get a girl friend back.
This is something people experience all the time especially if there is no formal breakup.
You need to work twice as hard if you really want to win her back. Not all the girls would jump into the relationship especially if the past relationship they had with you was a total mess.
It may take months or even years before she makes up her mind.
When the time comes that she goes back to you, make her feel more special and loved.
Be more affectionate and prioritize what she feels.
Understand her at all times and try to give her the space she needs if she asks for it.
Women like mystery and anonymity at times but when they feel that they need to know who the person behind it, you must tell her that it is you.