Here's a tip I just learned from having polish up one of my own stainless steel watches.
At first I used a Dremel with polishing paste, etc. Wasn't going so well. Then I found the video at the bottom of this post.
=> Just go to any drugstore, hit the Nails section, and buy a multi-grit padded nail buffer file.
(I bought the following one from CVS called the Beauty 360, for about $3. It has three progressively finer padded files, two on one side, one on the other. They're marked something like 1-file, 2-polish, 3-shine. The last two don't even feel like sandpaper at all. They feel smooth to the touch.)
Then use it as seen in this instructional video. It worked great for me. Good luck!
I bought one of those tough armor cases for this reason... I'll wear it "naked" for nice occasions, but for daily use I dont want to be worrying about accidental hits and scratches... Sorry to hear your situation...