Go over the whole tiled area with your belt sander. Don't try to take off the whole surface of the porcelain tile (you won't be able to), but just dull the shine.
Put on your rubber gloves. Mix one cup of trisodium phosphate in a gallon of warm water in a bucket. Thoroughly clean the tile with the TSP solution and a scrub brush. Use a sponge to rinse the whole area. Let it dry completely.
Apply a coat of sealing primer with your paintbrush, using straight, even strokes and avoiding drips. Let it dry for eight hours.
Apply a coat of flat paint in the same manner, keeping it thin and even. Let it dry to the touch; then apply a second coat. Apply a third coat if necessary. Let the final coat cure for eight hours.
Brush on a coat of polyurethane in the same way as you did the paint. Let it dry to the touch; then gently buff it with your 220-grit sandpaper, just enough to remove the shine. Apply another coat, and repeat the process. Add a third coat if the area is on a floor.