l run errands for my elderly mom, help her bath, make some meals, shovel for pathways, but l don't live with her.

Immobile, no. Housebound, yes. If she can feed herself and dress herself she can go to assisted living, even if she wears depends for a weak bladder. But if she is unable to get out of bed by herself, poops her pants or cannot find her way to the dining room, she is a nursing home candidate.