I don’t see the prescription meds for personal use as an issue for personal use. The prescription med police are not going to come out and dig through your pack. If you are the only one using them the others in your party may never find out unless you tell them. And antibiotics and real pain killers work where OTC pain meds do almost nothing.
I was in a motorcycle accident years ago and have lived with the pain every day, and I would have to take a whole bottle of aspirin pills to do what 2 real pain pills do.
The real pills could make the difference in allowing you to do what you need to do. And a few antibiotics could easily fight off an infection from a nasty cut before it becomes a real problem.
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You can run, but you'll only die tired.