I have a couple of felonies dating back 15 years will that prevent me from becoming a health care administrator

First where are you located? In US there are rules in medicare that prohibits anyone with felony or some other crimes from having direct patient contact. I know since I had patient contact when I worked as a tech, they did a annual criminal background and a sexual offender check each year.

So it may depend on the duties you were to preform and the type of healthcare facility. *if in the US, it wiould be hard to get this position, f that felony is showing up on your background search

Check with your potential employer. What are you doing now? Is it in a health field?