I think you'd have to be very unlucky to be stopped, and even then you'd be fine if you can prove that the meds are for your own use. Millions of people visit every year and there is no intention to dissuade people from coming. Unsurprisingly, the authorities are mostly concerned with recreational misuse, unlicensed supply and counterfeit products.
In case of loss or staying longer than anticipated, you should be able to get most things you need here, particularly if you have the original prescription. Thank goodness for 24/7 pharmacies and pharmacists who are permitted to prescribe a wide variety of meds.
Do people really fly around the world with important meds in unlabelled bottles ?