Honestly, I don't think you need medication. From everything you've described—your anxiety, physical symptoms and distress—are all very understandable considering your crazy-making family. Can a school counselor connect you with a therapist without having to get your mother's okay?

My therapist is the first one who told me that my mother shows every indication of having a mental illness; if I had known that growing up, and gotten outside support, I would not be nearly as messed up today (and on medication). You have a real chance to get help while you're young. I hope you can find at least one person to connect you with a therapist and/or tell your mother it's necessary for your well-being. But medication/psychiatrist? I wouldn't recommend going that as a first route at all.