If you are physically unsafe, your recourse is to call CPS. Emancipation is not granted on the basis of why you want out of the house, no matter what the reason is - it is granted SOLELY on your proven basis of self-support. Which you do not have.
Emancipation is granted rarely, and on the very, very few occasions that it is, it is granted to those minors who already have proven that they have both the income, and the self-discipline, to pay for 100% of their own support (rent, food, clothes, utilities, insurance, transportation, medical care, staples, school fees and supplies, and all the other incidentals of life) while still going to school and getting better than average grades.
I have a close friend who is bipolar, and if my daughter needed a place to stay I would not hesitate a moment to let her stay there. Being bipolar is not sufficient in and of itself to make your mom unfit to care for you. If you have called CPS and they have not seen fit to remove you from the home, there is usually a reason for that.
So, once more, in what way is living with Mom detrimental to your physical well-being?