http://www.youtube.com/watch?v=2XAqpOe9Zt4
Here's another good vid, from the Junkman. All the Junkman vids are good, lots of straightforward no BS talk about detailing.
Resorting to wet sanding, cutting-buffing on your ride will most likely as the junkman says, put you in a paint shop. You need to clarify, clean and smooth the top clear coat of your paint finish. The clearer and smoother this top coat is, the base color underneath will come though in all its glory. A clear coat is about the thickness of a postage stamp. Your vehicle is 12 years old, trust that there's not as much clear coat left like when the paint was new.
Paint shops can vary widely. The areas that been resprayed will likely have more paint, but then again only one way to truly tell, and that is with a paint gauge.
(hope you waited at least a month before waxing those freshly sprayed areas?)
A DA with mild finishing polishes, or at most a swirl remover Polish of the likes of Meguiars 205, Wolfgang Total Swirl Remover will be what you want you use to restore luster, gloss, and clarity. While Polshes like Meg's 205 can be used by hand it is a fantastic product, and works quite easily by hand, you will spend a lot more time restoring your finish in this manner. But good results can be had, by working one section-panel at a time.
Without a DA though, you will not achieve the same level of smoothness, and correction that a DA is capable of. Even the cheap $50 Harbor Freight DA with a good Backing Plate like a Lake Country 5" Urethane Plate, with some good Lake Country 5.5 flat Foam Pads will be light years better than hand polishing.
As for Clay Kits, the Mothers Clay Bar Kits sold all over the place like wally world, and comes with a pint bottle of spray lube works very well. Some now come with two bars, and the spray at about $20 or so for the kit. Remember, you drop the clay bar on the ground, you must toss it!
I'd probably wash well first with a good concentration with a decent shampoo like Duragloss, great stuff, smells like cherry, dry, clay, polish, and you will be good to go to apply a "good" sealant or wax, not that black box stuff! LOL
Let us know what happens?
PS: If all of this "DA" speak is too much for you for any reason, then yes, at least wash, clay, and perhaps try the Duragloss 501 Polish-Sealant like I suggested earlier. Keep in mind that while Clay will clean the paint (the Bar will probably be black after one section from the black box junk) a clay bar can instill fine scratches also to a finish. Many factors, the GM paint is generally hard, but still, depends on the user, adequately lubing the surface so the bar glides, not drags over the surface, what contaminants the bar can hold and be wiped across the paint. Most good detailers after they clay will then polish the paint.