i moved out when i was 19. my parents paid for most of my bills, as i only worked part time and went to school full time. you mentioned that your current living situation is not ideal for your health and that reason alone should empower you to make the step of living on your own. Maybe you could try out something that seems less 'extreme'. I could imagine that you would feel less anxious about it if you found a place not too far from your parent or moving into a shared flat. Sharing a flat has the advantage that you are never alone. I did miss my privacy but for me it was the ideal way of living in my early twenties because I enjoyed being around people every moment. Now many things have changed and I would prefer to have my own apartment and have my quiet space where I can relax.
You could make a pro/cons list but from your post you sound like you need to be around people your age. At the same time you feel responsible for your parent which is a difficult situation that most people your age don't have.
I'm not sure what to say about your parent except moving in a place close to him/her so you can visit regularly. Maybe someone else can suggest something.