Yeah, I'm afraid acetone wasn't a good choice there. Given that it removes fingernail polish, which is a form of paint after all, that should tell you that it would also remove any kind of coating on the phone cover, which is exactly what happened. I'm pretty sure the white streaks are simply what the actual color of the case is and it has a coating of black paint over it that you've now dissolved with the acetone.
For future reference, rubbing alcohol would be a much better choice in your particular case. Acetone, while it's good for cleaning circuit boards, is much too harsh to use on any part where cosmetics is important.
So yeah, assuming you're talking about a case that's meant to protect the phone and not the phone itself, then you've only got a couple of options. You can try to find something to use to repaint it like maybe a Sharpie marking pen or paint specifically made for plastics, but otherwise I'm afraid you're in the market for a new case.