Sometimes you just need to admit that you CANNOT fix things yourself, and at that point there is no shame in seeking professional help (not a hired goon). Ask your mother if she would pay for some counseling sessions, or pay for them yourself if you have a job, or talk to a counsellor at school. After a few sessions, ask your mother to join in a session or two. Then the therapist will make sure your mother doesn't scream at you and make sure you don't tirade against her.

It is obvious that you both love each other and mostly just need a neutral environment to work through issues. I wish you the best of luck, and my heart goes out to you and your mother. You will both be in my thoughts and prayers.