Does having Medicaid pay for private room in nursing home be medically necessary?

I am looking at nursing homes for my mom and she is basically refusing to move into a semi-private and I really hate to force the issue. I really do understand her reasoning not to want one. But Medicaid will only pay for a semi-private and I don't think we can afford a private room for her long term. One place I just talked to said it is $25 a day. Since they take all of her money to be at the nursing home, outside family members must come up with this payment.

I read Medicaid will pay for it, if medically necessary. Does anyone know what qualifies as medically necessary? As well as know the process for this?

My mom is 67, has MS, and needs complete assistant to transfer from bed to scooter, to toilet, etc. She sleeps horribly and gets muscle spasms and lots of pain at night, and is bedbound unless someone comes to help her out. She does not want to deal with a roommate on top of her own issues, knowing she is keeping them awake, as well as them waking her up.