As rasersk said, chlorine is a chemical put into tap water to kill living things, however, most areas of the country do not use enough chlorine to do damage like that to a fish, especially a well established Oscar. I would rule out amonia burns. As someone who has raised Oscars for a number of years, I've seen a lot of the diseases they can get, and by far the most common is, as lipadj suggest as a possibility, hole in the head, which is what I believe to be your Oscar's problem.
The most common place for hole in the head to attack is on the forehead, right between the eyes. If you divert your eyes from the two enormous white spots, as you mentioned, there is a hole in this exact location. The reason that hole appears darker than the others is becuase that area on the head has less flesh than higher up, where the two white spots are. Hole in the Head becomes a white spot when it is present in the fleshier spots, such as where your two main white ones are.
Hole in the Head is caused by poor water quality. Frequent water changes, not over feeding, adaquate filtration (strong enought to cycle your tank at least twice in an hour) and clean substrate are all great ways to improve and maintain water quality. But possibly the most important thing you can do is allow the good bacteria to build in your filtration. In my opinion, rinsing your filter media weekly, especially with straight tap water, is too often. Though the chlorine in tap water isn't enough to kill your fish, it is more than enough to kill the bacteria in your filter media. If your media is getting too full and clogging, then a larger filter is required, BUT, if clogging is the issue, I would rinse half of your media one week, and the other half the next and alternate in that pattern. This will allow the bacteria that remains in the unrinsed half to transfer to the half you rinsed and keep a healthy bacteria buildup.
The two chemicals that lipadj mentioned are good for Hole in the Head, but often difficult to find. Hole in the Head is fatal in most cases just because it is so difficult to treat. One thing i have had success with in the past is simply adding some salt to your water. No freshwater disease can exist in salted water. Unfortunately, I think your fish's condition has progressed so far that curing him is a longshot, not impossible, but a longshot. Good luck to you, keep us posted on how this turns out. Oh, and Oscars are big enough eaters that they will often continue eating until the day a disease kills them. Not trying to be negative or anything, just pointing out the facts. Again, good luck and i hope you are able to beat this!