Turns out my grandmother doesn't have Alzheimers, which is rather a relief! Over Christmas break the doctors and nurses at her new care center decided to do a few simple tests on her, based on the kinds of symptoms she was exhibiting, such as loss of balance, memory loss, and incontinence. The concluded that she might actually have hydrocephalus, aka water on the brain. They went and did a test procedure where they drained some of the cerebral fluid, and she showed improvement! So they went in this January and put in a full shunt from her brain to her abdomen, allowing the excess brain fluid to drain out. What was happening is that too much fluid in her brain was compressing it, causing many problems.
Today, my grandmother is doing much better. She can walk with a walker and a little by herself! I'm not sure about the other symptoms but I assume they've gotten better as well!