Polishing paint with minor imperfections

I have a dark blue 2011 Lexus IS with a minor amount of weird anomalies on the hood, and I can't polish them out by hand for some reason. They're almost like below the clearcoat if you will. You can't feel them with your fingertips so I'm kind of confused as to what to do. I've heard that not only is Lexus paint soft, but that I may still have a car that's painted from the factory in a two step, "non clear coat" type of paint job so I'm not too keen on any of what most people call "polishing". Already gun shy by this yahoo that attempted to buff my headlights and burned through my paint right there at the body panels edge by the headlight.

So in your guys' opinion, what should I use to clean up my paint? I'm ok with a few swirls left over that I need wax to hide, in a trade for thicker paint lol. I'm considering a pre wax cleaner, or a cleaner wax. Would any of these take out minor imperfections? And, is there anything I could use by hand to do this?

I've only my hand for now, and actually... I think I can get a practice car. What's the cheapest DA? I think when I looked up the recommended models porter cable came out the cheapest. Is that right?
Here's a semi decent pic of an example of the anomaly. From this photo it looks clear enough so that if you were to back away it wouldn't be noticeable but it is. It's actually a touch cloudier than this photo lets on. It looks like something dried on it and you could polish it out by hand but you can't. When you run your nail over it it's as smooth as the paint, as if it were under the clear coat. (if I have a clear coat that is lol)

Ok, my file upload keeps failing. Anyone have another way to upload a pic to this site?

Buster906 said:

Trying to remove swirls by hand is almost impossible. I use a dual action buffer for 99% of waxing and polishing I do. Do you have some kind of surface you can practice on so you can conquer being "gun shy"? Do you have a DA polisher?

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On post 3 of this thread https://www.autogeekonline.net/forum/auto-detailing-101/107273-soft-black-paint.html they talk about hand polishing. If it works there, can it work on my car?