Well, aluminum will not rust, so I'm pretty sure your safe there. But you can get surface rust on chrome, so use some good quality products that clean and seal chrome.
With your peeling, your probably seeing white powdery bumps under the chrome inside the wheel when it flakes off, and peels. Thats the naked aluminum oxidizing under the chrome. It wont hurt much, but the finish of the wheel.
You can do a few things.
1. flake off all loose chrome, and with a wire brush get rid of as much of the oxidation you can. Then you will want to seal it good, I would used clear nail polish, and paint the area well. (several coats would be a good idea)
2. have the whole inner rim sand blasted and painted, black, gray, silver are a few examples. This will insure all the oxidation is removed, and everything is sealed quite well.
With this problem your having on the outside, you have a very good chance its doing the same thing on the inner rim, such as under the tire. This can cause a poor bead, and a leaky tire. The GF had some Eagle 077's that were doing this not even a year after she bought them, and we had the whole inside area blasted, and painted at Eagles expense. (since they were back ordered and this was a cheaper solution than warrantying them out completely)
~F~