Paint Job on Case

I'll give you my personal opinion:

It's unnecessary to use any type of rubbing compound on a new finish except to correct some type of minor application problem. And even then, only when a hardener additive is used in the paint. Same goes for the hand glaze which is usually used to remove swirl marks remaining after compounding. Exactly what paint product, including any additives, did you use? I am assuming an enamel of some sort. I am curious as to why you were told to use a compound though. There really should be no need for it. If you didn't use a hardener, the only way you will get a decent gloss back is to repaint (and you could have to strip everything first to avoid lifting).

Rod

Yes, compounding will remove overspray. But...if you didn't use a hardener, it will also remove much of any gloss that you may have had; permanently. With an unhardened enamel the film is too soft to regain a high gloss by further compounding and polishing. A rough surface is usually indicative of either a dry spray or excessive orange peel. Both are the result of improper application, either in materials or technique. Depending on the severity, those problems may not be resolved with just compounding either, even with a hardened enamel or urethane. If you did use a hardened enamel or urethane, you might want to try some color sanding first with something like 1200 or 1500 grit to smooth out the surface and then compound to bring back the gloss. This of course assumes you have enough thickness of film to do this without going through to the primer. In any event, with no hardener you are unlikely to get to the finish you want without repainting. Sorry, but I think that is just the hard facts. With no hardener being used, you have to get that paint on right the first time with no significant application errors. Repair work after the fact is pretty much a futile exercise; at least if you are looking for a decent glossy finish.