First, take him to the vet (but I'll bet you already have) to make sure it is just a sprain and not a joint out of socket or something else. Keep him as quiet as possible, trying not to let him jump too much. If you can get him to lay on a heating pad turned on LOW that should help with the pain. Alternate that with holding him in your lap with a cold pack on the sprain. Heat and cold therapy helps that kind of injury heal more quickly. The thing that will help the most, though, is lots of love and affection, which I know you are giving him in large doses.
Let us know how Luke is doing.