I got a sinus infection while at WDW. You are not allowed to have a prescription filled out of state unless your doctor is licensed in Fla. It's a Florida law, so they told me when I tried to do this. So, even if you have a prescription paper from your doctor, it will be useless. If your home doctor will oblige to write a prescription, get it filled before you go!
There are walk-in Centra Care centers near WDW. The walk-in centers are first come-first serve and for me, it took three hours of waiting then 5 minutes with the doctor. By the time I got to the pharmacy to get the antibiotics and back to the resort (thank goodness we had rented a car), we lost 4 hours that we had planned on being in the parks! DH, DS, and DD all waited for me with an afternoon swim while I was at the doctor, but we were all sad to be apart even for the 4 hours on our family vacation!
Also, when I knew I had the sinus infection I did find out the information for the doctor that will come to your hotel room. It costs minimum $350 for a visit! That was when I decided to go to the walk-in care. The front desk of the resort was very helpful, and if you don't have a rental car, they will somehow arrange transportation for you, if nothing else, the resort's courtesy van. I did not find out the transportation details though because we did rent a car.
Hope everyone is healthy for you when you go on your magical trip!