You don't have to like every student. Every student doesn't have to like you. The student you describe may be immature. Dealing with immature behavior is part of your job. You are dealing with kids, after all. This particular kid really gets under your skin. I don't think you getting angry with this kid will improve anything. Try to maintain a professional tone.

Trying to diagnose this girl as autistic is really not your place. It sounds as if she genuinely dislikes you. That's her perogative. I think you have to become okay with that.

If this is high school, then your students did not volunteer to be in your class. They are compelled by the law and their parents to be there. So that can lay the groundwork for resentment in some students' minds. Maybe the other history teacher was better than you. This student is trying to blame you for her not getting the grade she wanted. That's immature on her part. But I don't know that it rises to the level of "malevalence."

Saying you want to "put her in her place" does have a condescending ring to it. It sounds like this is more a matter of your pride being hurt. A power-struggle with this kid will get you nowhere. Is this student a person who gets along well with peers? Or is this an awkward kid with few or no friends. This kid probably has a problem that has nothing to do with you. Teaching kids is a tough profession. You need to be sensitive to them, while also having a very thick skin. It must be challenging.