Something similar happened to my cat four years ago. My lab was doing a "butt-tuck" around the living room like a mad dog and Aussie tries to make a run for the cat tree. Well she gets almost all the way to the top and doesn't quite make it, so she falls about four feet down and hits the edge of my brick harth. She started hissing and ran to the bathroom and up where her food is. I immediately ran to her and noticed her back right leg was just sort of hanging there. Thinking it was dislocated or broken, I immediately ran her to the vet and they took x-rays and showed nothing was broken. The doctor told me that sometimes when they injure that area they will not use their leg because it's just too sore.
This could be the case for your kitty, but I don't think I would take any chances. It turned out that my cat had a spinal cord injury.
They couldn't diagnose this right away but over the next few days she lost more functionality. Day two her tail had become completely limp and day three she could no longer hold her bladder. They had to stop the meds they had given her and put her on something else. It took about 6 months but she did finally recover.
It doesn't sound to me like your cat has a SCI since things seem to be improving, not getting worse, but I would still plan to take her as soon as possible to be sure. If nothing else they will probably give you some pain meds to help him over the next few days. I'd rather play it safe than sorry.