This isn't going to clear up by itself, it's going to take some persistence and patience (and lots of bleach) on your part. You are doing the right thing to keep the chlorine up, but you really need a current CYA level to know how high to take the chlorine. What that CYA level is will also determine whther or not you should consider draining some water.

The chlorine you're adding to the pool will kill the algae, but the filter is what gets the dead algae out, so it must be working in order toclear up the pool. Do you see particles returning to the pool through the returns? If so, you will need to replace the cartridge.

Janet