Can You Get Emancipated Based on Your Parent's Illness

My question involves juvenile law in the State of: Michigan.
I am 16 years old, homeschooled all my life and unemployed. My mother has PTSD, and lupus (I am usually her care aid when her lupus symptoms hit). My father isn't around to support me or my siblings, we see him every once in a while but he doesn't provide money to my mother to care for us. My mother is a very strict military sergeant, courtless times when she is angry at me, she calls me swear words (b*tch, H*e, motherf*cker etc..) she has been doing this since I was a young child, she tells family members that she does it so when someone does it in the future when I am an adult, it doesn't effect me but right now it is effecting me and upsetting to me. When I am sore or hurting, she doesn't provide care for me, I have to get myself up through the pain and beg her for medicine. She is currently enrolled in online schooling and she makes me do her work for her all the time, and I can never get to do my own work (I am currently in the 12th grade). She has told me if i make her mad enough she will hit me and won't stop (she hasn't hit me before) and when she is angry with my father, she comes and yells at me about it.
Considering I'm living in this condition, am 16, homeschooled and have no employment record, can I get emancipated from my mother?
Right now I am at my grandmothers home because my mother puts me out the house alot for days at a time, and then picks me up from my grandmothers.

Not a chance. You need to show that you already have proof of fully supporting yourself.

If you are being abused, call child services. Perhaps Mom could ask Grandma if she'd take custody of you..