Death in dreas is not like it is in the waking world - it's actually more about the loss of an old self for the birth of a new self. The other girl was simply a part of yourself you felt you need to get rid of. You feel terrible because on some level there is still a mourning. You did, after all, destroy part of yourself. If this girl was in a cage, you should ask yourself why you were repressing this part of your personality. I wouldn't worry too much on the death in this dream. It's simply time for change

:: Questions to consider ::

What aspects of your personality did you feel you shared with the caged girl?
How were these traits something that you felt needed to be kept in check...or held in and repressed?
Why do you now feel as though this part of yourself needs to be destroyed?
What traits did you see in the third person in the room (that took care of the body)?
How are these shown in yourself? How can these strengths help you handle overcoming this change?
What traits do you want to replace the dead ones with?