Is there a program that would pay me to take care of my disabled sister and have her stay with me while she is on dialysis?

Some states pay a small stipend to those who stay home to care for disabled relatives or spouses. There are generally strict requirements for qualifying as "disabled" and some income restrictions apply. Contact your state department of health and welfare. You don't indicate her age, but if she can't work, she might qualify for social security. An elder care or family law attorney might be able to help you with the social security and state stipend but DO NOT fall for one of those high fee "guaranteed" schemes. You should only pay by the hour. Your best first place to start - and cheapest - is to look at the web site for your state and look for "disabled benefits" or "care giver stipend" something like that. You can also learn a lot by going to your local state office for health and welfare. You'll have to spend some time waiting in line but you can talk with a live person and have a thorough discussion.
Good luck.