Not sure where to turn, father will need long-term care soon. Any advice?

Hi All, I'm 50, single, and have lived with my father for over 10 years. We live in an apartment and share rent and expenses. Its been helpful to both of us as he gets a little less than $2000 month from SS and we get along well and keep each other company. The problem is he's been declining over the last 5 years, exhibiting signs of Parkinson's. After doing some research, I think he actually may have Lewy Body dementia.

The neurologist doesn't really tell me anything as far as diagnosis but my father definitely shows signs of dementia. He can't tell time anymore, doesn't know the day of the week. He needs more and more assistance getting to the bathroom and has fallen a half dozen times. I have to work 6 days a week, long hours (retail) so he's alone during that time. Up until recently I've felt he's been OK , but now I realize he needs someone to look after him when I'm not home. The doctors he sees haven't really been helpful. Both of them sent out the hospital home health care nurses, but all I get from them is "we can't help you", Medicare doesn't pay for our services. Why would these doctors send these people out when they can't help? We can't afford to pay for private help. So I asked the nurse from home health services what I should do, call nursing homes? and she said yes but in unsympathetic tone she said "yes, but let me tell you they cost on average $13000 a month and want the first months deposit upfront". Well of course he or I don't have that.

My father is on Medicare with Medicaid but not full Medicaid. I'm not sure how that all works. All I know is my father can't be alone anymore, I can't be with him because I have to work, we have no other family support, we can't afford home health aids, the people from the local hospital have not been helpful and my father is likely to need a nursing home soon but trying to get him into one is too much for me to handle and he doesn't have that kind of money. Not sure where to post this, skilled nursing, Medicaid or dementia.