Mom with Alzheimer’s constantly claims she's “sick.” Anyone experience this?

Sounds as if she is scared with all the symptoms of the aging process and nearing the end. Depressed? Anxiety?

Yep - her kidneys are failing because she 'goes to the bathroom too much.' Doctor number 1 does not know, so she must go to Doctor number 2....
She does not go to bed - she much prefers to let everyone hear about it every two hours or so!

She spends way too much time alone and in bed watching TV. She is on week two of insisting she is sick. Additionally, it makes it hard to know when she is REALLY sick. She gets herself into a huge panic. She called me last night panicked saying she has the flu. She doesn't, I talked to the NP on staff. I tried to tell her not to panic, that its just the flu and she should feel better tomorrow. That seemed to help a little bit.

In the mood stages, PWD tend to obsess in things. Once it gets in their mind it sticks. Maybe just try distractions..."I'm sorry you are not feeling well. I will help you get up and fix you some nice warm tea (or soups, or...)" Then once she is up just try to keep her moving a bit.
I also don't know if it hurts to spend a day in bed 😁