What happens if someone was dealing with post acute withdrawal syndrome after quitting alcohol, would the doctor possibly prescribe anxiety medication?

Depends: Your primary care provider likely will not. That person ought to seek out a medical detox unit, where they can medicate the person after they stop alcohol, it can be life threatening withdrawal if the amount of alcohol is high enough, and needs to be monitored and medicated as needed, otherwise they could development delirium tremens and/or withdrawal seizures.