Short of going with a full machine polish, something like Swirl X is your best bet. If you'll be applying by hand, try it on a specific spot first to see if you feel like the results are worth the effort.
From now on, try to clay in one direction only. If any hairline scratches are introduced, they'll only be visible from one specific angle. Also, make sure your microfiber is up to snuff. Get a ton of good ones and switch them out frequently. Use a spray detailer when you dry the car to add a little bit of protection against unintended swirls and always keep your wipes linear in a consistent direction.
Black is a bitch. There's a good chance the swirls were there before you cleaned your car, you just couldn't see it until it was shiny. Resist the urge to 'overclean' as even the most careful cleaning will introduce a few minor swirls here and there.
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