Cool field! Airplanes and healthcare? Who could ask for more?
There is much that lies within this field. Air Ambulance services flying helicopter med-flights to hospitals. Larger services transporting patients in fixed wing aircraft. Volunteer services that coordinate with the aviation community to transport sick patients throughout the country. Some companies are call-in centers, specific to aviation. The major airlines and business aviation uses these services. Then, there is a myriad of manufacturers of aviation medical equipment.
As far as advancement is concerned, may I suggest that you refer to the U.S. Bureau of Labor Statistics Occupational Outlook Handbook. That will show you the trends. My belief is that much of your advancement is dependent upon your attitude and how much you enjoy doing what you do.