Quick remedy for screen and back scratches?

So I did a lot of digging and found out that toothpaste (or in my case, SOME toothpaste) relieves the minor scratches on your phone. It didn't work for me. So is there any other way to really relieve the scratches on my screen and on the back of my phone besides installing screen protectors?

Also, can I use car cleaning products to remove scratches on the back of my phone?