That sounds like a really awful living situation. Does your father know that you plan to move out in a few months? Is there any chance that he would step up to the plate and support you to prevent that from happening?

From your post, it sounds like your mother is verbally and emotionally abusing you. And, yeah, I would doubt her diagnosis of all your 'issues' if she's the only person making those claims, instead of some kind of doctor.

Is there anyone you could talk to, like a counselor at school or teacher or some other adult you trust? Moving out at 16 is a big deal and discussing your options with someone else would probably be helpful. Some schools have resources for kids who have to leave abusive homes.

The problems in your family are not your fault. They aren't going to go away just because you leave. Your parents will find something else to fight about. They may even keep fighting about you, even if you are not there!

You may find it interesting to google 'golden child scapegoat.' I think you'll find some similarities to your own situation.