How can I restore the shine to my shower tiles?

IF you have been using any SORT of abrasive cleansers-- you more than likely have WORN OFF THE SHINE from the surface glaze & that is totally un-repairable ... sorry for that bad news. It happens with really old porcelain sinks-- look dull and dirty even tho they are "clean as a whistle!"

use a buffer...like what car detailers use.

Well, I’ll sure use a buffer. They have a white color to them which is baffling

I've read that car wax like Turtle Wax is supposed to be a temporary fix to shine up tiles and shower doors... just be careful not to was the shower floor, it would make it slippery.