I'd possibly try different shampoo, and waxing it after polishing. Polish removes grease, dirt etc, as well as stripping away a tiny layer of the paint’s top coat (damaged or oxidised sections) - which reveals the fresh pain beneath. Car wax protects the car's paintwork, so when it's buffed in properly, the car gets a brand new protective layer making it look shiny and new for longer, and keeping water off the paintwork.

The best thing to do is wash your car normally with whatever products you use, then have a look at the paintwork to see if you actually need to apply polish. I'd only polish it after washing, and before waxing, if I saw there were problem spots.