This is really harsh but it’s good advice. I’ve never checked important medicine but I never really thought about the danger of losing access to it in a random city. Fortunately I think local pharmacies would be pretty understanding in this situation… and give people temporary access to missing medicine… hopefully… perhaps the airport could even act as a middleman (I got urgent care drugs at a foreign airport once when I was sick).
Pharmacies cannot and will not do that (except for insulin, for which it's now allowed in some states, and maybe a few other non-abusable things.) If it's a controlled substance -- which includes most things you'd be worried about withdrawal from -- forget it. If it's a more tightly scheduled drug, you'll have trouble even getting an unfamiliar doctor to prescribe it. It's not that they don't care about your withdrawal syndrome, but they generally care much more about not losing their license.
I think it would be a matter of calling the prescribing doctor’s office, explaining the situation and giving them the details of the pharmacy you’d like to pick up the prescription from. The biggest hurdle would probably be insurance, who doesn’t want to pay for more medicine than was necessary.
Good luck with that Dec 24-26 (the time frame we're discussing). You might get an answering service that can get a message through to your doctor but the office is likely to be closed and empty. Then you still have to find an open pharmacy with your medicine in stock.
I don’t know that pharmacies are allowed to do that. What you usually have to do is call your primary care or other doctor and explain the situation and have them send a prescription to the new city