What is the first step in deciding to find nursing home care for my Mom?

She is 96yrs old, lives alone. I am next door & take care of her. She has lost most of her hearing; she eats mostly sweets; drinks Boost protein drink, re fuses to bathe herself or let me do it, refuses to change her dirty clothes. Everything is a battle for me, so I'll just give up and go home. She tries to keep partial dentures in her mouth, but their's nothing for them to attach to. Dentist said they could not full dentures for her because of protruding bone in roof of her mouth.