Many state Medicaid systems have a program that allows a Medicaid beneficiary like your mother to stay at home and receive paid home care from a family member. These family caregiver programs, sometimes called Cash and Counseling or similar name, can pay you an hourly rate to care for your mother if she qualifies for home care from Medicaid. The pay is roughly the same as Medicaid would pay to a home care aide who worked for a Medicaid-certified home care agency.
If your mother qualifies for such a program in your state, ordinarily she would get to choose who the paid family caregiver would be; her decision, though, would still be reviewed by the Medicaid program, to make sure that it is legitimate. The same thing is probably true in this case. If you have a properly executed durable power of attorney for finances, that might make things a bit easier because it gives you the legal authority to make financial decisions for your mother. But the Medicaid agency may still need to approve you as the paid caretaker. Since you practically live with her and are already taking care of her, you would be the logical person to become the paid caregiver, and it's very likely that Medicaid will approve.