What is up with this girl? I need serious help?

So I am 23 and I met a 44 year old lesbian. (She looks and acts much younger..) But anyways, I developed a crush on her. In the beginning, I kind of wanted her to leave my alone because she'd be calling and texting me CONSTANTLY. Like seven times in a row calling, and she'd get real mad when I didn't answer right away. She also made it a point to tell me how jealous her ex is of me, and allowed me to cuddle with her, etc. Then I finally texted her that I liked her, and she said that it would be "immoral" of us to date because of the age gap. I told her that I couldn't have her coming over anymore then. (She was "dropping by" constantly. It would be too difficult for me. She got real mad, came over to my house, and got into a verbal fight with me, which landed in her physically attacking me. Then she turned around and told my grandmother (who raised me and didn't have a clue I was gay) that I liked her. She kept refusing to leave and finally I gave her all of her stuff and she left. I have been so depressed. But then today she called my house because my phone is shut off and asked my grandmother how I am doing. Who does that? What is wrong with her. Does she like me and is afraid to confront it, or what? And yes, I know she's crazy, but I actually miss her..