One way is to file a a petition in the probate court in the county where your mom resides. If you can prove she is a danger to herself the probate judge will issue an order and the sheriff will pick her up and take her to a facility for evaluation. You need to get help from an attorney who has experience handling this kind of case. Best of luck to you.
Georgia has a Department of Children and Families where one can make reports when a person may be a danger to themselves or others or when there is abuse. The department will send someone to investigate and if the representative finds evidence of problems, the state will act. Reports are annonymous - so your mother would not know you made the report. There are also local agencies that take reports. It's doubtful that there would be a commitment - but there could be an evaluation leading to a commitment. As an alternative, consult a guardianship attorney who should be familiar with the state guidelines.