Like the others have said, this happens more often than it should.
My mother always loved my oldest sister more than the rest of us. According to my mother, my oldest sister could do NO wrong.

And that feeling of my mother's made my oldest sister EVIL.
I digress. LOL I'm so sorry you've been treated this way. It isn't fair and your Mom is SOOO wrong. Children should be loved equally, and they should KNOW that they're loved equally!!! That's how I brought my kids up. Both of them know that I loved them to death.
I agree with the others that it would be a good idea if you could live with your Grandmother, if she would let you. No one wants to feel unloved or uncared for, and it sounds like your grandma would be the perfect person to live with, as long as you can help her out. Could you?
Please stay away from the drugs and alcohol -- they WILL kill you, and I don't want you to become a statistic -- PLEASE. Young people are dying at a very high rate from drugs & alcohol! Please stay away from it.
God bless you and please take care of yourself, okay? Hugs, Lee