Maybe a child shouldn't say such cruel things, but a parent should, first and furthermost, never be cruel towards their own child. You expressed your true feelings, and that's okay. You have every right to feel the way you do - you're a person too and are allowed to have emotions and feelings. You are also, even moreso, not responsible for another person's happiness. Your mother might be sick, but as sad as it is, you are not responsible for her mental health or wellbeing. You are already trying to take care of yourself. It's okay to feel upset and frustrated. It's okay to be angry. It's okay to tell someone "Enough." It really is.
I understand why you'd feel guilty. Trust me, I've been there, hardcore. I've been upset at someone for the longest time but felt so, so guilty for being angry, because they couldn't help their behaviors - they were sick. But I realized, being sick is no excuse for making me feel like crap and treating me like a doormat. I'm a person too.
I know things are hard Snow. We're here for you however we can help!