OP: Have had success atleast 3 times in the last 18 months, with challenges we have faced due to my son's accident in Rome, Italy July'12.
You have to call Delta Customer Service to cancel your ticketed itinerary.
Explain your health situation. They will ask and document the Problem/ Reason for change, ask and document Dr's name and address and details of the hospital etc.
There is no need to have a desired travel date now, when you cancel.
But please remember to save and file away the DL ticket number for the flight cancelled.
Not the PNR but the Ticket Number is required when you are well to travel.
Then again call Delta CS. and make the new travel reservation.
You should not be charged any change fees, but you will have to pay for fare difference (if any) between the fare of the original ticketed itinerary and the fare of the new itinerary.
Strongly recommend you call as soon as possible.