Welcome, I see you found your way here.
They don't have children's wheelchairs to rent, only adult ones. Like teri mentioned, you can probably get one to borrow from your resort if you are staying on site. A pillow from the room might be helpful to fill up the space a little and keep him in place a little better. You can keep a wheelchair with you in all lines/shows until just before boarding the ride. You don't need any special card or anything to bring the wheelchair in.
If you ride the WDW buses with a borrowed wheelchair, I would suggest he get out of the wheelchair during the bus trip if possible. The driver does secure the chair with tiedown straps and there is a seat belt for the wheelchair occupant, but your son will be too small in the chair for the belt to really do much good. My DD stays in her wheelchair, but she has her own wheelchair that fits her.
If you have a stroller at home that he still fits into comfortably, you might want to bring it along. If you use a stroller, you can go to Guest Services in any of the parks and get a Guest Assistance card that will allow the stroller to be treated as a wheelchair (ie, it can come in any buildings, lines, etc. the same way a wheelchair would).
If your doctor suggested pain medication, keep it along with you. You probably won't be able to get any in the parks. And if the doctor said to take it on a regular schedule, do that. It will help to keep the pain under control better. If he gets tired (but not tired enough to leave the park for the day) you may want to try First Aid. There is one in each park and they have nice, dim, quiet cubicles with cots in them that he could use to rest. They also have RNs in First Aid that could help with advice if you have any questions..
