You still have more of the shower arm stuck in the drop eared elbow.
I usually get them out through the existing hole in the wall or, make it slightly larger but still small enough that the escutchion will cover it then by catching a piece of the thread and break it inward then grab it with pliers or, small vise grips continue round and round carefully breaking it inward without breaking it off. Kinda like opening a sardine can... It ends up looking like a helicoil and it comes out. Hopefully this works for you, there are other more expensive methods if this doesn't work.
On the siouxchief website http://www.siouxchief.com/Frm_MS.cfm click specialties, then tools... Scroll down to "Internal Nipple Wrench" That is another tool that may work.
Another way that I get them out is by using a #7 easy out with 1/2" cut off the end.
If you can get it using the first method you don't have to buy any tools.