If you can document the illness then you could take that up to the school and see if they would consider academic forgiveness. Especially if this class was taken a while ago and your grades are up to snuff now. I would contact the professor also. Make sure you call during business hours, sound very professional, are clear/concise, etc. Sob stories will only get you so far--take responsibilty
for your actions. That is a good quality to have as a hopeful-nurse.
We all make mistakes (esp. when we are ill or are having major life problems/emergencies/issues). Some people are more understanding than others. I think Daytonite has a point, yet no one is infallible! I think mercy should be extended, yet there are limits (and in nursing school, there isn't much mercy to be had). If your record proves you to be a good student and this is a one time situation, then it's reasonable to hope! If not, you CAN retake the class and replace the F.