Sounds like maybe slow blood flow on that one side. It may be like when you sleep wrong and your arm "falls asleep". I would take the dog back to the vet just in case there is a clot on that side preventing the blood from flowing properly. Not unusual for humans to have the same thing after surgery. That is why you have to wear the stocking after surgery to prevent clotting.
My dog had a stroke and it's entire right side was numb. It is coming back now but it's front right paw is still numb. May want to make sure your dog gets the proper excercise and give an asprin for pain.