When we redid our kitchen we put in a new porcelain sink and within days we started getting the sliver scratches. I called the manufacturer of the sink and they told me to you have to purchase a special cleaner for it. I don't remember the name of it because we have since moved and I have stainless now, but it was like a miracle. You just rubbed it on the spot and it was gone.
I got it at home depot or lowes in the cleaning section. It is in a metal square can, and it has a pink background with writting on it. Ask someone that works there and they should be able to help you out. Oh and make sure you open a window when you do it, it does smell. Good luck!