Hi there!
The labrum tear/ inflammation/ flare is more likely to cause pain while throwing a ball, while bursitis is more likely to cause pain when the hand is not elevated. Yes, a cortisone shot may be associated with increased pain and discomfort for the initial few days before it finally settles down.
Hope this information helps.
Take care!
Also, would a cortizone injection give you more pain on your shoulder for days after the injection?