I think my mother might be getting alzheimers, but she won't see a doctor. Is there any way to find out if she has it given she refuses doctors?

Possibly. Alzheimer's is a diagnosis of exclusion, with the only definitive way of confirmation being a post-mortem exam of the brain. But the mini-mental status exam is useful as a screening test. A score below 24 out of 30 means a more thorough exam is needed. Clinical exam would be useful to exclude treatable causes of dementia.