Welcome to DC! Dalmore's right. To do any effective job of removing them, you should invest in a orbital buffer. The Porter Cable 7424 or the other model are used by many people (myself included) here to remove them without worrying about damaging the paint. If you have a little more money to spend, you may want to buy a Cyclo. This is a 2 headed orbital and some say works better than the PC. It's a bit more though. Read all the threads you can, and absorb the knowledge here, and you will be amazed with your car when its finished! If you don't want to invest in a orbital buffer, then you can try to fill in the swirls like Dalmore said. Meguiar's ColorX is one that can be found at like a Checker's or Autozone. I'm sure others will also have some suggestions for you.