about 10 years ago, I was the Human Resources Manager for a small firm. The small size of our business meant that we were not subject to many of the FMLA rules...but here is what I remember about it.
Since you work for a hospital, I'm sure that your place of work would almost certainly be subject to the FMLA laws.
Assuming that the law has not changed, it seems like you would qualify if you feel that your illness is preventing you from doing your job. If your doctor supports you and is willing to write a statement to your employer, all the better.
From what I remember, your hospital will have to hold your specific job, or a very similar job, open for your return for a specific period of time.
FMLA is of course a tough decision, because of the lack of a paycheck. However, there is a reason the FMLA act was created...to offer the employee protection from firing should they need to leave their employment for a period of time.
Start by talking with your doctor, and also by researching the FMLA laws. Here is one link. Best of luck.
http://www.dol.gov/esa/whd/fmla/