What do I do so I can be the one who gets paid for taking care of my grandmother as her caregiver?

Natalie, the vast majority of grown children who are caring for a parent or grand-parent are not paid..... unless that parent/grand-parent can pay you from their own pocket. As NeedHelpWithMom had written, you would need to draw up a caregiver contract.

Another option is if your Grandmother is on Medicaid [which is different from Medicare]. Most States have some type of program where a family caregiver can get paid. But note, it won't be anywhere near what you would earn in the outside world. You could be paid minimum wage for a few hours each week. Medicaid is taxpayer funded, thus each State handles their own rules and programs.

A couple of possibilities. Write a caregiver agreement and have her agree to a fee for service.

Is she a spouse of a veteran? Seek veteran spousal benefits and become a paid caregiver through their organization.