Check with social worker at facility. Medicaid under usual circumstances will not pay for a private room. Or call medicaid to ask what policies may apply.
If mom has dementia she is probably better off to stay put. Even moving to another room could throw her for a loop.
Here in MN neither facility my MIL was in allowed a Medicaid patient to have a private room, no matter what. In her first facility she entered on private pay, then shortly after that she went onto Medicaid. The facility didn't have an open Medicaid bed so we were forced to pay the additional $600 per month to cover her private room (for over a year) or she would have had to move out. This was in a non-profit facility that was very inexpensive compared to others.
This idea won’t help with cramped, but maybe will if this situation is problematic because the roommate is causing issues for your mom. When my mother was in a nursing home, most of that time on Medicaid but even when private pay, she had a roommate. The nursing home was kind enough after seeing that our family visited daily to place her in a room with a lady who, sadly, was completely bedbound, nonverbal, and slept most all of the time. The nurses and aides would come in and quietly take care of her. She very rarely received a visitor. It was a very sad thing to see the lady in such a position, it also made the room quiet and peaceful. Maybe something like this could make your mom’s life better
If mom has dementia she is probably better off to stay put. Even moving to another room could throw her for a loop.