I totally agree with
sm1ke.
Take advice from someone who has done a lot of body work during his life-time. Me.
In fact, within the past few months, I did some cosmetic body work on the front end of my 2016 MX-5. I repainted it and then put on at least 4 heavy coats of clear. I didn't have any body damage. I just wanted to remove the large "M" emblem which entailed filling the large recessed area that the "M" is imbedded into.
Never use rubbing compound unless you plan on having your vehicle re-clear clear coated. Rubbing compound will remove your clear coat before you even realize the damage you have done. It happens very quickly.
I recommend using very soft cotton cloths for this polishing work. Nothing beats cotton for great finishes and don't press heavily while polishing. Use very light strokes. It will take a bit longer but will be worth the time spent.
As sm1ke said, using Meguiar's polish or something similar is the way to go and even with that, use sparingly until you see the shine starting to show. Remember, the clearcoat finishes on most vehicles, including Mazda vehicles is very thin. Once you break through this finish, the painted, or colored surface is dull by nature and can only be fixed with another coat of clear.
I suspect what you did just caused microscopic scratches that appear to be flat or dull but under a microscope you will see they are actually very fine, scratches.
If possible, use a florescent light at an angle to see how your work is progressing.
Good luck and hopefully, you will post before and after pictures.
Sorry for the long winded post. Sometimes my enthusiasm gets carried away.
