Using just one polish won't get you a decent/long lasting finish. That paint needs to be hit with a dedicated swirl remover, then polished, then sealed.

Personally I'm a big fan of the Poorboy's range of polishes. From the Poorboy's range I would start on your paint with a couple of passes of SSR2.5 with a light cutting pad, then another pass of the SSR2.5 with a polishing pad. Then I would use SSR1 with a polishing pad, then another pass with the SSR1 with a finishing pad. That should remove most if not all of your swirls. Then I would polish the car with two or three passes of polish (I like the Poorboy's Pro polish) and then seal the paint (again using two or three coats) with either a Carnauba Wax (for excellent depth of shine but it won't last very long) or with a synthetic sealant (for excellent protection but not as much depth as a wax).

That should fix all of your problems. It is a long and frustrating job, but if you polish properly you can make a decent paint job look extraordinary.