Not androgyny- definitely. Androgyny is the lack of any gender, which she doesn't have. She also is probably not a hermaphrodite, (which is what you meant, when she has male parts? I think) as doctors would've noticed before now. I really don't think you need to worry. She sounds perfectly normal.
Honestly, she probably was masturbating. Kids often rub against things innocently because it feels good. It isn't necessarily masturbating like you would think of an adult doing it, more like scratching an itch. She doesn't know what it is.
Is she using bubble bath or anything? That can sometimes be irritating to the genitals, especially for girls.