I felt so bad for you as I read your story. I know what it's like to miss out on a childhood because of a parent's behavior. This is just far too much for you to deal with, and it isn't necessary!
I don't have any words of wisdom, only that wanting to have a happy life and to arrive at adulthood with some degree of sanity of your OWN is not selfish!!!
Have you talked with your dad about this? What does he say? He's your father and should want the best for you...just like your mom would if she was well. (Do you think she'd be happy if she was aware that you were suffering so much because of her?) Tell your dad what's going on...you aren't betraying her in anyway (unless he's pure evil and would use the info to hurt your mother.) DO NOT cut your father out of your life to keep your mother from becoming depressed. There will always be something to depress her until she gets the right kind of help.
Does she have a doctor? It doesn't sound like it, but if so, you need to talk to the Doc to make sure he/she has the whole picture. Ask your dad to go with you. If your dad has limited resources or isn't sure what to do either, you can check with your county mental health services to see what options are out there. It's unfortunate we're living in an economy where it's likely these services have been cut-back.
If nothing's coming together for you or you can't make the connections you need, talk with your school counselor. If there's a teacher you particularly connect with, talk with that person. (Do you know how outrageously OLD this advice makes me feel???
I would have considered it really lame when I was your age.)
My main point is that though you aren't a kid anymore, you aren't an adult yet and you shouldn't have to take on these adult duties. (I'm not even sure an untrained adult should be trying to care for an un-medicated bi-polar person. Is that really best for the patient?)
Adulthood comes soon enough, and when you get there there's just no going back. You DESERVE to be happy and to spend your teen years doing what teens do (within reason and always safely, of course!)
DO NOT feel guilty. DO NOT become your mother's enabler. (If she wants to live outside of the mental hospital it might just have to take her medicine.) KNOW THAT YOU DESERVE HAPPINESS AND PEACE.
I know...so easy to say, so difficult to do. But it can be done, and it can be done while you still love your mom.
I wish the very best for you, Melody.