I live in NY and my mother is sick and disabled. She is 69 years old and doesn't want to go in a nursing home. I cannot afford to not work

See my recent discussion topic - NYS Medicaid Waiver program Nursing Home Transistion and Diversion program. If she has Medicaid, or can get on Medicaid, you should be able to obtain enough services to keep her at home

Try getting her in an assisted living place. It is not a nursing home but a small apartment with meals served and medical care. They even have microwaves, small refrigerators No cook stoves. They check on you and clean the rooms change the bedding etc.
Or try a health care organization. Where I live there are several with varying degrees of care offered. From around the clock to just some house keeping. Or someone to sit with her while you are at work