Hi, I'd like to help you with your question.
It sounds like your mother is playing favorites here and not giving you what you need, which is equal care and love, creating your feelings of hostility towards her.
There could be two things going on here. Either one, your mother loves you and is unable to show it due to psychological issues, or two she purposely avoids showing how she feels about you.
Often when parents act a certain way toward their children, they learned the behavior in childhood. When it comes choosing favorites and withholding love, your mother somehow learned this behavior is acceptable, either because it was done to her or she witnessed it done to someone else. Only a person with a severe mental illness such as sociopathic behavior would choose to act this way on their own. So most likely, your mother was a victim herself. That does not excuse her behavior, but it helps you to understand where it probably originated from, and therefore it has nothing to do with you.
If you have tried talking to your mother about how you feel and have gotten nowhere, you may just need to stay away from her as much as possible. She needs to have insight into her behavior to realize that something is wrong so she can seek help. If she does not have insight, then the likelihood that she would keep treating you this way is high. Since you cannot change her, then changing your reaction is the best option.
You can also ask her to make clear boundaries in how you are supposed to contribute to the household and how much your sister contributes. Make sure it is written down and posted so you and she can be clear.
Is there anyone else you can stay with? Maybe an older sibling already out of the house or a close relative? Even a friend?
Do you have a job? If you are able to, try to find a part time job. It will keep you out of the home and provide an income so you can save to leave home.
Is it possible for you to move into the dorms or share student housing?
Even if you only have 9 more months it may be worth the effort and expense.
Consider counseling to help you cope. If they have therapists available on campus, take advantage of the service. If not, try asking your doctor for a referral to a therapist in your area.
I hope this has helped you,