The "half" knee replacement you describe sounds like a unicompartmental knee replacement (UKR). Sometimes only one side of the joint needs to be replaced. A special implant has been made so the whole joint isn't disrupted.
Even with a partial replacement there is still a certain amount of inflammation and swelling that goes with it. It usually takes about six weeks for a surgically-induced trauma of this type to heal. This means the inflammatory response is resolved and the tissues return to normal.
Most patients find that although they are just getting back to their pre-operative range of motion (ROM), their function is much better. Knee ROM will continue to improve over the next six weeks.