How do I get my sister diagnosed? She lives alone in the city. She is a retired teacher. I live in another state.

When was the last time you saw your sister? Do you know any of her friends or neighbors?
You could call the Atlanta Area on Aging and see if you could get information on a wellness check for a vulnerable adult.
I have a friend who did this to check on her sister after her sister’s husband died. My friends sister had been contacted by someone who appeared to be grooming her for financial fraud. Her sister was severely depressed, didn’t have dementia but was very vulnerable. She lived in California and my friend was several states away. She was able to get her sister help. That’s been a couple of years now. Friends sister is still living alone in Ca but she’s getting medical care and communicates with her siblings. Here is a link from this site with a number you could try.
https://www.agingcare.com/local/atlanta-regional-commission-atlanta-area-agency-on-aging-ga

She has no other family? I’m afraid the only way you can get her evaluated would be to go visit her and set up an appointment with a geriatric psychiatrist. I understand there’s quite a wait, so you may want to do it now. If she doesn’t want to go, speak honestly and with love to her of your concerns for her well-being.