I recommend you go check out www.autogeekonline.net Plenty of info on how to fix this, and what's up. It sounds like you have wash induced swirls and spiderwebbing. Being new paint was it baked on, or left to just cure on it's own? If so, I suggest you not wax or use a sealant for at least a month so the paint can out-gas properly.
The short run down:
Ditch the Absorber and Terry Cloth towels. Use microfiber towels (I suggest the stuff at Autogeek). The Cobra stuff is thick, and will trap dirt not removed in the wash deep in the cloth away from the paint.
Next the two bucket method with a Grit Guard in each bucket. Make sure these buckets are used only for washing, nothing else, this way it keeps extra dirt out of your wash water.
I suggest the higher end sheepskin mits, the utili-mit, or a microfiber chenille mit for use on the paint. Something that holds a lot of soapy water and also helps pick up the dirt and trap it deep in the mit suspended in the soap, away from the paint.
Always wash in straight lines, wax in straight lines (not applicable if using a PC, UDM, Flex, or Rotary), and either blot dry, or blow dry the car. An air compressor is your friend if you have one.
Also a little trick to use when drying your car, if you're starting to get water spots, use a quick detailer with your drying. Spray it on the panel you are drying (still wet with water), and then dry. No water spotting will occur.
Good luck
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