It's going to take time to filter out all that material. The pool didn't get in that condition overnight (years) so even if the process takes a month, it's very quick in comparison to how long it took to get in this state. Keep brushing and stirring it up.
You could examine the sand in the filter by opening it up. If it looks really nasty and caked, I would try the deep clean procedure first.
http://www.troublefreepool.com/threads/73192-Deep-Cleaning-a-Sand-Filter
DE is useful, but I wouldn't go there yet. Get some on hand if you want to try it later but wait until the water is more or less cloudy and you can start to make out the bottom.