I am downright surprised I haven't seen a YC startup that performs this sort of medical tourism brokerage to be honest. Take this business model! I'll be your first angel investment.
I know the insurance plan that Utah government employees are on will pay you to go to Mexico to get your prescriptions filled. Airfare, hotel, and medication costs are all covered. Free vacation just so the company doesn't have to pay the US prices for drugs.
Edit: This is true for India which is a top medical tourism place:
https://www.orfonline.org/expert-speak/implications-india-me...
https://scroll.in/article/931857/with-20-medical-professiona...
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC404528
http://www.who.int/hrh/resources/16058health_workforce_India...
No, really: you just, flat out, made this up.
You have no way of knowing that demand for services in every single country with medical tourism outstrips supply of professionals. You just assumed it.
If it doesn't, which is just as likely (I think more, but I also don't know, and unlike you I won't pretend to know), then you're injecting money into the local economy, while getting medical/dental care at a lower price: win win.
The US has a uniquely onerous path of education and accreditation for medical professionals, with substantial supply-side limitation in the form of slots for medical school. Other places aren't so burdened.
Something to think about.