One trip both my kids got sick (very sick, high fevers too) at different times. My son turned out with an ear infection, and my DD had strep throat. Both times it was late at night when their symptoms showed up, and I was at the Dolphin with no car. My DH wasn't with us either.
The front desk gave me the number to an urgent care clinic that will send a doctor to your room. They were the best help! They sent two doctors each time, along with a huge bag of basic tests, and many common prescriptions. So my kids were seen, tested, and given medicine right in our room! It was great as my son was so sick, so he could lie in bed while we waited for them. The cost I paid directly (about $300 plus per visit) then they gave me all the paperwork to submit to our HMO. I was (surprisingly) reimbursed completely! I honestly would have paid that out of pocket for how quickly they showed up, they checked out my kids so thoroughly, and my kids each were feeling so much better by the next morning.
If you ever need them, they are East Coast Medical Network, 6000 Turkey Lake Road, Suite 209, Orlando FL 32819. 407-648-5252. I keep their number now with me! They will come to any Disney area resort I was told. I asked even if someone thought they had a broken bone or something; they told me that they have a van with an xray they would drive over even! Wow.