You can buy certain meds over the counter here. However, may be you should ask your primary care provider in the US the best way of obtaining them. You might be able to get a prescription for six months or even a years supply at a time, carrying with you in hand luggage with written permission from doctor, and then refilling when you return for a visit.
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"There's this thing called being so open-minded your brains drop out". - Richard Dawkins