Sorry to hear about your accident. Renting at the parks is probably not a good option since you will need it at the resort too and some of the rental areas are quite a way from the parking area.
Here are the links to all the sites that DIS readers have reported experience with. All of them will rent
ecvs or wheelchairs and will deliver them to your hotel.
Care Medical:
http://www.caremedicalequipment.com/
Walker Mobility:
1-888-726-6837
www.walkermobility.com
RANDY'S Mobility is in Kissimmee 407-892-4777
http://randysmobility.com/
Colonial Medical
http://www.colonialmed.com/about_cms.html
The advice about renting a wheelchair before you go is actually a good idea (although you don't have much time to arrange things). You will probably need a wheelchair to get around in the airport, so if you don't bring one with you, call the airline and arrange for a wheelchair for each part of your flight.
Wheelchairs are sometimes available at your WDW resort, but they are first come, first served and can't be reserved.
ECVs are more expensive to rent, but do give you more independence. ECVs don't have any way for you to elevate your foot if you need to. A wheelchair is a less expensive option, but someone will need to push you. You should keep your crutches with you. For some rides, you do need to get out of the wheelchair and the crutches can make your transfer a little more steady. Here's a link to the
DIS site info on Mobility disabilities in WDW. It includes prices for renting from the parks and info about rides.
If teri repsonds, she has some great links to wheelchair/
ecv info from previous questions/answers on the DIS. Otherwise, look for one of her posts and follow the links.
PS. You don't need any proof to rent a wheelchair, but it might be a good idea to bring your ER report along in case you have any problems and need the information to explain to a doctor what happened.
Also, in case you get tired and want to lie down for a while, there is a First Aid Station in each park. They are cool and dim and have cots in individual little cubicles for resting.