For years now, showerheads have been required to discharge only 2.2 gallons of water a minute. Not much water, but it is enough. Anyway, in most showerheads, it's a small round disk with a tiny hole in the center, and is removable. It should increase...
I would be tempted to use a car buffer and brass polish. Shouldn't take that long. After that, you might want to research a lacquer to seal it in and prevent the oxidation from coming back. I know they do that with brass ornaments you get from stores...
that'll probably backfire. Most deodorants have something in them to kill bacteria. Body spray, depending on how "sweet" it is, might feed them and cause more odor than you want...and not the kind of odor you want either. There are all types of deodo...