Perhaps, explain to FAFSA your condition via written letter and show them proof that most of your money goes to your mother's medical bills. Maybe, some receipts, and doctor's written medical diagnosis, and personal bills? I mean it's a lot of private information that you may not want to tell them, but it's worth a shot? And see what they will say?
You could also ask your dad to be a co-signer, or a trusted friend? OR you could borrow your dad's or trusted friend some money, this way you don't have to pay interest :), or maybe a discounted interest 🙂 These are just some of the things I would try if I were to be in your shoes.