I'm actually hoping to be in a similar situation someday... I'm an International Studies major doing my pre-reqs for nursing school. I've done some research (probably not enough) on world health and such.
Here's a few organizations you could look into:
Peace Corps
International Committee of the Red Cross
Doctors Without Borders
It takes time to apply to all of them, and most need a Bachelor's. You also won't be sent to the prettiest places on earth, and in some cases not the safest. Most are between 6 months to a year being outside the country, and in some cases you won't be paid because it's all volunteer work (you'll probably get a stipend).
But if you're committed to making a global impact, and gaining great experience go for it.
Good luck.