As a young'un I was taught to use the world "medicina" too. However, in the USA since the eighties, the word "medicamento" started predominating in patient handouts for Spanish speakers. At first I thought it was just more Spanglish, but when I checked it out with some of my parents from the Mexicantown neighborhood of Detroit, they confirmed that "medicamento" is indeed the favored word for "medicine" in Mexico and in the USA. How is it in other Spanish-speaking countries?
(Like it or lump it señor Trump, Spanish is already a local language like French is in Canada--and we are better for it!).