Blessed:
When the financial aid office at your school puts together your financial aid offer, they are already including an allowance for your room and board.
If you've been living at home, up until now, that allowance has probably been fairly small. Schools assume that students living at home are saving a lot of money compared to those who live in the dorms, or those who live on their own, in off-campus housing.
If you're going to be changing your living arrangements for the coming school year, be sure to contact the financial aid office, and let them know. They'll take that into account when they analyze your financial aid eligibility.
HOWEVER - as you are probably already aware - moving out of your mom's home is not going to change your financial aid dependency status. If you're a dependent student for financial aid purposes now, you will remain a dependent student, regardless of where you are living next year.
Your dependency status will only change when you either marry, turn 24, or begin providing more than 50% of the financial support for your child.
While financial aid (which includes student loans) is designed to help college students with the cost of a place to live and food to eat, there are no forms of financial assistance that are intended to help a student move out on their own. From that perspective, no, you're not going to be able to get a "school loan" that will enable you to pay rent.
Contact your financial aid office, so that they can analyze your financial aid need as an 'off-campus student living alone', rather than an "off-campus student living with family", and you may qualify for some additional assistance next year.
Unfortunately, you're going to have to have money to move out of your mom's home. Financial aid is not going to get you there.
Good luck to you.