Where do I sign up to be a caregiver for my mom who's 83 years old?

Unless you have a private agreement with mom and she pays you, no one pays you to caregive mom. You more or less just get stuck doing it for free.

Now - maybe you'd better keep your job, if you have one, and let someone else take care of mom.

This is not a care agency. Call your Medicaid office and see what they offer. Some care agencies work with Medicaid. They will train you, hire you as an employee, and allowbu to care for Mom.