I think it's key to learn some basic Spanish before learning medical Spanish
There are things you can google online to find resources for Spanish medical interview, but if you don't learn basic sentence structure and verb conjugation you will have a VERY hard time understanding the answers they will give you to your questions
Before doing immersion, find something online to read or an intro to Spanish course, be sure you've got a basic understanding at least in principle, you will learn more in the country if you get that much on your own
One thing mentioned that is wrong above is about Quito. Ecuador is now one of the best Latin American countries to learn Spanish. It's come a long way from 12 years ago. The Spanish spoken there is considered some of the most clear and enunciated, much closer to what you would learn in school and phonetic (that will not be the majority of what you hear in the States but when first learning Spanish it is helpful to start easy). Due to better economic conditions it is more stable, tourist friendly, and a more modern state, Quito especially, but that has raised prices, but still fairly cheap compared to US at least. Definitely not cheapest in South America but if you want a safe, easy to travel in, cheap place to learn Spanish, I recommend it. Still plenty of language schools there. As far as tourism, if you ever wanted to go to Galapagos Islands, you must fly through Ecuador that is the country that owns them. You can visit the Amazon jungle, one of the few places where you can swim in the water and no risk of schistomaniasis, but still mosquitoes and risk of yellow fever. Quito itself is so high you don't have to worry about any mosquito borne diseases or bug spray!! Ecuador is also home to coast, amazing seafood, and Peru is close by for Machi Piccu etc. All by cheap bus. The weather is much nicer than Central America. People like to go to Costa Rica and Panama for language as they are big on tourism and financially and economically stable (so safer and easier to get around if your skills aren't up to it). I agree you want to avoid tourist areas but you also want to be safe and be in areas that gringos can navigate while acquiring skills.
Asidd from inmersion (there are online programs to go to Ecuador or elsewhere, and medical Spanish programs can be found) other excellent ideas are tuning in to Spanish television, watching movies originally in Spanish (part of learning language is context and lip reading), radio.
Meetup website has opportunities for getting involved in a Spanish language club.
Attaining conversational level Spanish will make it so so much easier to pick up medical vocab than just piecemeal route memorization.
Obviously other systems like Rosetta Stone or audiobooks or whatever is good too.