IMHO, the best thing to do first before any correction is visit the documentation and how-to's page and watch all the Mike Phillips Videos.
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The terry cloth would have been good during a restore of a single stage paint but not for clear-coat. That plus the shammies are what got you into this jam.
The videos will show proper washing techniques using the two bucket system and proper products, along with videos on dual action buffers, pads, claying and proper scratch removal techniques.
Drying can add more scratches if not done correctly. Use high-end products to dry such as The Guzzler. Lightly prime your dry towel with a QD spray.
Clay using premium clay and a clay lubricant
When removing scratches and swirls always start with a test spot first!
Also, always start with the "least aggressive product".
A PC7424xp along with a Lake Country Pad starter kit is the perfect dual action (DA) buffer package to start with. It rotates and oscillates and is perfectly safe. Follow Mike's videos.
Start with a cutting pad and (for example) a Pinnacle Scratch & Swirl Remove. Watch Mike's video's for proper technique.
Next step would be a finer polish (i.e. Pinnacle Advanced Finishing Polish). with a polishing pad.
Lastly using a softer finishing pad apply wax. You should see results instantly.
If you don't have a lot of time, you can always start with HD Speed which is an "All in one" (AIO), Scratch/Swirl Remover + Polish & Sealant (synthetic wax). You should get great results from that.
Lastly, take lots of pictures and be sure to post them here so we can all marvel at the great job you're doing!
