Mom lives with me. Is there a way that I could receive an income to stay home and take care of her?

Not really. You can check the rules for your own state as to being paid to care for a family member who is diagnosed with a need for your help. The pay is terrible. The job is 24/7. You lose all abilities to hold and get a job otherwise. It is mentally and physically and financially quite devastating to caregivers. You know that if you are here on Forum for any time at all.
You can explore getting paid to care for a family member by accessing on the top line of AgingCare, the aqua and blue line with your avatar picture, the little magnifying glass. Press on that and you will find search. Type in getting paid as caregiver, or follow the alphabetical letters for subjects that interest you. From there follow the rules for your own state, discuss assets and ability to pay with your Mom, see an elder care lawyer, and follow up gathering all the information you need so you have more with which to make your decisions.

Check with your Area Agency on Aging to see if they know of any local resources. Generally speaking, elders should be paying from their own funds for care. In some states there are Medicaid waivers that will pay for a few hours a week at minimum wage. If a veteran, they may qualify for VA Aid & Attendance.

Here is good info right from the home page of this forum:

https://www.agingcare.com/topics/133/paying-for-care

Also, if you make an arrangement for your mother to pay you for her care, make sure you have a written contract so that it doesn't disqualify her from Medicaid, should she ever need it.

The fact that your mother is paying bills implies that she has funds. She should be paying you room, board and for her care.

In some States, folks who are poor enough to qualify for Medicaid can enroll in a waiver program which will pay a caregiver a pittance.