Why don't you ask the programs that interest you about job placement of graduates.
OHSU for example has a big program. You can also poke around the AMIA website for job offers and meetings. AMIA just created a board subspecialty in informatics, so if you finish medical school you can go that route and end up CTO of a hospital.
A lot of the real development jobs are done by companies, and the in hospital work is a lot more about tech support, resetting passwords, network management, help desk, etc.
If you want to develop systems and code, look at the big companies like Epic, Cerner, and all the smaller companies and see if they are hiring and what requirements they have. Then you can see what you need to have.