Looks like simple clear coat damage. Either you can search the web extensively and learn enough to work your way out or pay someone to buff it out for you, which may be cheaper in the long run. I would suggest some polishing wax one or more tries before giving up and paying someone. Lesson learned. Move on. It doesn't look time sensitive, take your time and fix it correctly. Good luck.
I agree with the previous poster. Looks like you have enough clear coat left to deal with what you left behind. I would use a clean, soft, slightly damp cloth and something mildly abrasive, like 3M Scratch & Swirl Remover for light colored paints -- don't press hard, let the S&SR do the work. It'll bring out what looks like an oily haze. Use a clean soft rag to buff it smooth at that point, try some absolutely non-abrasive wax on it to see what it looks like. You have so many of those spots that you should be able to experiment several times until you get it right. You might be able to progress to a lightweight electric buffer once you've figured out what to do. Good luck. Cheap lesson: NO ABRASIVES -- EVER. Things look a lot different dry than they do when you're washing them. Somebody earlier brought up Zaino. That used to be the only thing I'd put on my Corvette, back when I could afford the gas. It did a superior job protecting the paint, came back to life with very little effort.
Ouch! I've seen people wash cars with old jeans before and that made me cringe. Yes, please take it to a pro detailer with good reviews on yelp. I've taken my truck to a ''detailer'' that went super abrasive on my tailgate to try to remove some scratches. Wool pad + rotary + high cut compound destroyed it. Ever since then, I've done it myself after some research.
