You do not have to actually sue to become emancipated, Victoria. You can go through the Division of Family Services to apply. If you have a job, bring proof of that job, and you would have to show you have a place to live that is affordable on whatever salary you make. My niece emancipated after her mom died and her dad moved out to the country to become somewhat of a recluse.
To catch up on your education, you might be able to do a college-high school double credit program, where you sign up for your regular HS courses, but take the courses at a nearby community college, so you get both a high school credit and college credits at the same time. If you are emancipated, you might even qualify for the PELL Grant to cover living expenses, books, and college costs. Since you are so young, I recommend you keep a private journal where you can sort through all of your tumultuous feelings or any leftover resentment you might have towards your mom---it keeps things in balance.