Is it time for a nursing home?

Lately I have noticed, Mom does not take care of her daily needs. She would get up out of bed and use the bathroom, and then wash herself with a washcloth. I have noticed for several days now, that the washcloth has not been used. Likewise she does not seem to be changing her bladder control pads, nor going to the bathroom. She eventually does, but it's usually late in the day. When I ask her about it, she gets angry and says, " I went to the bathroom and washed myself". Then if I prod her, she says " If you don't want me here, I'll go somewhere else". She does not mean to a nursing home! She says she will get her walker and go to a hotel. I honestly don't think she knows what she means. Then when I try to talk to her, ( she is very deaf ) she will say " I don't know what your saying". I don't know if she can't hear me, or she doesn't understand what I'm saying. She gets angry very easy. I have suggested getting someone to help her with bathing, she said she would kick and hit them, if I brought anyone in. I don't know what to do. Another thing that drives me crazy is she will sit and talk to herself out loud. When I answer her, she will say " im not talking to you". Then she also sits and stares at the clock, counting out the minutes. She does this every night starting about two hours before bedtime. Her doctor doesn't think she has alzheimers. Says " it's just old age", and dismisses it. I need some advice, and obviously he's not going to give it to me. She is on a health plan, so I have to use their doctors. When my father was still living, they had an excellent doctor thru his work related healthcare. But now that he is gone, she no longer has that.