Steroid injection can be a very helpful treatment for some conditions. Bursitis is often the cause of pain and limited motion in the elbow. An inflamed joint or bursa can respond well to a steroid injection.
Keeping the elbow joint quiet for the first 24-hours has one distinct benefit. And that is to keep the steroid in and around the joint. Movement, especially turning the palm up and down, disperses the antiinflammatory agent.
This means it seeps out of the joint. The body then absorbs it and the effect is much less than intended. So give yourself the extra time in hopes of a better result out on the court or on the golf course next week!