My 92-year-old mom fell in Assisted Living on Friday & went to the hospital to check out her head on Tuesday. She complained about her left and and the x-ray shows fractures. Does she need surgery?

Well, mom needs surgery on her left finger. It is a compression fracture & dislocation, and they said she would have pain the rest of her life without surgery.

First, notify her doctor. Some factures are more serious than others.
If it is a simple hairline fracture, docs usually leave it to heal on its own. It takes some time and makes movement painful. But it will eventually heal.If it is more serious, she may need immediate attention.
I haven't heard of surgery for fractures unless they are affecting muscle tissue, etc.
Also, I would enquire as to why she fell. Was she left unattended while standing? Where the bars to her bed left down? etc...
good luck