iPhone 5 scratches :(

So, I've recently bought an iPhone 5 on the apple webstore. I've been very carefully with it, but it fell off my bedside table while I was asleep and it's full of tiny scratches now.

I have searched the internet for ways to remove them, and found some ways to remove them (like toothpaste, polishing, and lens cleaning cloth), but I'm not too sure if I should try any of those things, because I've also heard that those things can damage your oleophobic coating.

What should I do now? any ideas? or will the scratches become invisible if I put a screen protector on my phone ?