As you say, you don't have anything at all to feel guilty about. You are endangering your own health by continuing to carry such a heavy burden.
I think it's past the time for asking for help -- obviously, that doesn't work. I would just
tell your father that you are not physically or mentally able to care for your mother and sister any more. Tell him he is welcome to talk to your doctor if he doesn't think your illness is serious. Tell him about your depression. Tell him that the time has come to put your mother in a memory-care facility or hire in-home help since nobody else will help with her care. Tell him that you are unable to care for your sister and that if they won't help, they're going to have to come up with another solution for her, too. Tell him that you have done your best, and done it without help, and you just can't do it any more. Tell him how much it hurts you that nobody else in the family cares enough about your mother, sister and you to help, and how alone you feel.
If you could go back to counseling, that could be a good thing for you. Obviously, standing up to your family -- especially your father -- doesn't come easily to you but, until you do, they're going to keep taking advantage of you. Counseling might help you get over your undeserved feelings of guilt and find the strength to stop your family from running over you.
I suspect that part of the reason your family is so unresponsive about this is that they have no idea what a hard and stressful job caregiving is. They may think that you and your mother sit around and watch TV all day, and you fix her meals, and that's about it. Whatever the reason, though, they're obviously not going to suddenly jump in and help you, so it's up to you to insist on a different arrangement.
Good luck to you. I'm so sorry you're having to deal with this unhappy situation.