If POA, would that give me authorization to decide what medication my mom takes?

Are you a physician?

No. The person with medical POA (healthcare proxy) has that authority if Mom is no longer competent to make her own decisions.

I would want this to be a decision made with a doctor.

Here is a good explanation of documents that authorize making medical decisions:
https://www.agingcare.com/articles/legal-documents-to-make-healthcare-decisions-for-your-parent-146623.htm

No. Your job is not to micromanage someone else's life. It's simply an "overseer" kind of thing, set up when a person can no longer take care of their financial or personal affairs.
The term is used pretty loosy-goosy around here and I honestly don't KNOW what each individual interprets it to be. For legal clarification, look it up.