Long term care insurance?

I'm 26, and take care of my mother who is 53 and she will be 54 in October. She has FTL dementia. Over the past six months, her mental capabilities have declined a lot. She almost set my apartment on fire. So now, I keep the detachable burners in my room and the bedroom door is locked when I leave the house without her. And the oven's mechanisms are locked. She's now only allowed to use the microwave when I'm not home to cook for her, or I supply her with pre-made food from the grocery store. She's forgetting common words now, is incontinent, and has visual and auditory hallucinations at night, up to three to four times a month, they worsen if I have to go away for a night. I will be blunt. I'm not the caregiver type, and my relationship with her has been strained since I was 17. I've discussed it with her, and we both feel assisted memory care living would be right for her. She wouldn't be stuck watching TV all day and she might get something out of day to day life again. Her older sister, who has lost her ability to use words and speech due to dementia, is in a facility already. They cost $5.3k a month. My mother really wants to be with her sister. I contacted to facility and they said they don't accept anything but long-term care insurance. But the long-term care.gov site says people with dementia don't qualify for it. I only have about 3 months of care saved up for a place like that. She receives SSDI, but it's no where near enough, and she has no assets or savings and her credit is crap. Three years ago, when I started to care for her, I called APS on her, because of her violent mood-swings. She has since calmed down due to an anti-depressant, and pseudobulbar affect has given her a happy-go-lucky personality (which we aren't treating, I wouldn't be able to deal with her violent behavior that used to be her original personality). Sorry, went of topic. APS gave us a case worker who couldn't help us much, she did give us an application for long-term Medicaid care (I honestly don't remember). We filled it out and sent it in. She was denied due to her not having SSDI yet, but they told us to reapply after she was approved and that she would get it. Her SSDI case had to go to trial and it took a year before we could get it. By then, APS had closed our case. I've looked and looked, but I can't find the application they gave us and Agency for Aging sends me on a carousel of phone numbers to call, that eventually lead me back to them. I have no f***king idea what to do now. Short of me becoming a best selling author within the next month and making $30k in one go, I don't know what to do.