Definitely sounds like a bit of an obsession. Be very careful about who you add on facebook and who you are communicating via internet. Make sure you have explicitly expressed to her that you are in no way interested in maintaining contact and she is not welcome to contact you. There's always measures you can take if this turns into a real stalking situation, although right now it sounds like she is an emotionally insecure/dependent person and is just being disrespectful.