This sounds like a troublesome relationship already considering that you have only been going out for a month or more. If indeed what you say is true, I don't see your relationship lasting very long unless your girlfriend can face the fact that she's got some issues herself.
If I were you, I will leave her be and let her stew on a problem that doesn't exist. If she really loves you then she'll realize that this "three month cooling off period so you can get over your ex" is just so silly and childish.