I travelled to Australia last fall with sufficient meds for myself. Prominent in my purse was a letter from my doctor listing the prescriptions and a letter from my pharmacist listing the same meds. I understood that the purpose of the letters and lists was to permit me carrying these meds in my carry on luggage.
Clearly the letters also served a purpose all border guards would understand. & both my doctor and my pharmacist know about it.
The pharmacists said: "We prepare people to go to Florida and other states for 6 months each year."
There is your lesson - documentation.
:C