Can an 18-Year-Old College Student Get Custody of a Younger Sibliing

My question involves a child custody case from the State of: New Mexico & Illinois

I will be 18 in about 2 weeks, and I am going to University of Illinois full-time in the fall. I will be moving into a new apartment with my grandmother. I have a younger sister who is 13 years old. We live with our biological parents. They have an awful marriage; my mom has been cheating on my dad since I was 12 years old. My mom and I don't have a very sturdy relationship; I'm the oldest, so we're constantly getting into fights. She is an alcoholic, but refuses to get treatment. She gets drunk on the front porch every night and stays there until about midnight when she goes to bed. With my dad on business trips almost weekly, I've been forced to take over as caretaker of the house. I do all the household chores, I make meals for my family, and I've been paying bills since I was 15. When my mom and I get into fights, which is often, she is emotionally abusive and, if she's really drunk, physically abusive. Ever since I was 14 and was serious about making sure I get to college and get out of the hell hole, my little sister would come to me crying, telling me that she doesn't want to be left alone in this house because she knows that my mom won't take very good care of her. Please don't get me wrong, when my mom is sober, she is bright and funny and helps out. She is a mom and she loves us. But she's only sober for about 6-8 hours a day. My sister is the golden child, and she NEVER gets in trouble. Ever. So, when I leave, I believe that she will be okay.
With all of that said, for the past 18 months she comes to me, crying and begging for me to take me to IL with her. So, my question is that I was wondering if there was any chance I could get custody over my 13 year old sister and take her with me to Illinois to live with my grandmother and I while I go to school? I personally believe that she will be okay if she were here alone. It would be very hard for her, but she would be safe. My other question is that if I can't take custody of her when I turn 18, can my grandmother?
Thank you SO much for any advice.

Both parents would have to be proven legally unfit. The standard of acceptable parenting is depressingly low - and nothing you've said here would rise to the level of "unfit".

If you believe there is abuse or neglect, contact child protective services.

Have you considered asking your parents if you can take your sister with you? While it is extremely unlikely you would be able to force the issue, if your parents are willing, your sister can live with you and grandmother.