You need to call the regular number you called to make your reservation as soon as possible with your request.
In the past, Special Reservations/Special Needs has not dealt with guarantees for ground floor rooms. They only have dealt with rooms that were special in some way - like a room with special features to deal with a disability. I think that is still the case, so if you call them, they will tell you that first floor requests can't be guaranteed.
Call the regular reservation number and request a 1st floor room for Medical Reasons. You want to say that particular phrase because the room assigners fill those requests first before similar requests that are not for medical reasons. You also want to make that your first request if that is the most important to you. Doing that puts the information in the computer, where it will be available to the room assigner. This information is from WDW room assigners who have posted on the DIS Boards and from what I and others have been told in phone calls to CRO and DC Member Services.
Depending on what resort you are staying at, 1/3 to 1/2 the rooms might be first floor anyway. So, even without a request, you still have a high likelihood of getting first floor just by chance. That's also not a real common request - a lot of people want higher floors because the view is better or they feel it's quieter.
Phone calls or faxed requests won't hurt, but may not make any difference. Phone calls to the resort don't actually go to the resort; they are answered in a call center (although the CM answers with the name of the resort as if they were at the resort.) The person answering just accesses your information that is already in the computer. Some resorts don't accept faxes at all and just throw them away (DVC has written that in their member newsletter many times and has for no faxes to be sent).
Room assigners have posted in the past on the DIS Boards that they sometimes received several hundred faxes each day and it was not possible for them to match those up with reservations, so they were thrown away unread. Other room assigners at resorts that received only a handful of faxes have reported they did take faxes into consideration because there were few enough for them to do that. We don't know at this time whether faxes are actually going to the individual resort or are also going to a call center.