I have mental illnesses and by being with my narcissistic mother they become worse. Can I move out from her home if she hurts me mentally and emotionally while being available to help her when she needs?
Yes.
(However, if you have a mental illness, this would be on the condition that you are able to care for yourself and live on your own, or else that you will have the required support and assistance. Since mental illnesses vary in nature, this may or may not be relevant to you personally.)