A few comments:
Those internal "turtle" filters are lousy. Unless you are dealing with a hatchling, they can't keep up with the amount of waste a turtle produces. You need an external canister filter or something similar that can really turn over the water volume of the tank multiple times per hour. There's a great thread on filter media that also talks about sizing:
viewtopic.php?f=9&t=30145The cloudiness may not be a factor of poor filtration as much as a bacterial bloom as your tank cycles. Google aquarium cycle for lots of detail, but basically a fresh aquarium is establishing various types of bacteria colonies which help to deal with the nitrogen waste in the tank. A common step in that process is a cloudy bacterial bloom that lasts a few days.
Most importantly, though, your tank is too small. You either meant 12 years old or 12 inches long. I'm assuming it is 12 years because you probably could not fit a 12 inch turtle in a twenty gallon tank. How big is your turtle, measuring just the shell with a ruler, not curved along the shell? The general guide is at least 10 gallons of water for every inch of shell.
A RES needs space to dive down and explore. It doesn't have to be a tank, it can be a large Rubbermaid container. You'll also find that a larger volume of water to dilute turtle waste, actually makes it easier to deal with cleaning and water changes. I know water changes, and water parameters, are much easier to deal with and less infrequent in the 55 gallon tank I have than they were when I had a 20 gallon. And, Tobi was less than a third the size when she was in the twenty gallon, but I was having to do more frequent water changes.
