Swirls are just fine scratches. You need a really fine compound.
Do you have a buffer? I use what I call 3M stage 3 compound
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Then use a soft finishing foam pad. Like the least aggressive from any of the "kits".
My method that worked best when I detailed cars at a dealership was to put a real small amount of compound over the affected area and turn the RPMs on my buffer to about 1/2 of what I'd use normally to get out scratches. Then I'd use very light pressure on the buffer and keep it as flat as possible and buff out the swirls. Just the weight of the buffer should be enough to get the job done. If you're having to wipe off a bunch of compound afterward, you used too much compound. The pad should erase almost all the compound by time you're done buffing the area.
Afterward just make sure you don't ever take it through a car wash or use a terry cloth towel on the paint. I'll use a "water blade" and a microfiber to dry. Just remember to apply almost no pressure to the microfiber or you'll start to swirl it again.
