Do you mean, "mess" as in your living conditions? There's nothing to be ashamed of.
I'm glad you emailed someone at your county already. Since you list your location as Nevada, I found the DHS page you need:
HCBW_Prog
I would focus on getting your sister "social adult daycare" so you can clean up your house and get a mental break from taking care of her. Believe me, social workers are well-trained for walking into caregiver's homes and seeing a mess. When I was my mother's caregiver, I had to do everything by myself and sometimes her large 1-bedroom looked like a tornado hit it. Because I was too exhausted to clean it.
You need to take your focus off of how your sister and family wronged you. That is something a therapist separately from your sister's care can help you deal with.
Right now, reframe your situation is getting help from the county to take care of your sister until you can move her to a nursing home. And that's precisely why the Alzheimers Association and county social workers who deal with the elderly are trained to help you.
But your mindset right now is 100% focused on the wrong thing; how YOU feel wronged etc.,. What you are experiencing is called "caregiver" burnout. Until you get the county care in place for your sister, you will not be able to fix this situation for you both. I know I sound harsh but that's not my intention. I come at you with compassion and experience. I went through this with my own mother. It was not easy.
Here are the offices you need to contact:
Contact:AgingDisability
Here is the chatroom forum for caregivers, on the Alzheimer Association's website. Here you can post your story with your sister and hear from others who are in your situation. They can offer you emotional support and ideas too, esp. if they live in Nevada. It's about connecting yourself to the community around you, to get the help you need for you and your sister.
https://www.alzconnected.org/
Good luck!!