Ryan,

I have sand, not DE, so cannot comment accurately on the filter. That said, NO filter should be putting ANYTHING visible in your pool....you should only see clear water returning. Other will advise on how to inspect/correct your filter problem but you do have a problem.

Secondly, apply your Cl dosage at dusk, when the Sun is off the pool. It will be very effective against organics when there is no Sun to kill it. With no CYA, you should bring your Cl level up to 10-12ppm at dusk and then test the next morning. Any drop in Cl during the night will indicate that you're still fighting algae. (don't be surprised if most of it is gone). Repeat that procedure each evening until your pool is clear.

Are you holding off CYA for a reason?

Since you have not posted test numbers, I assume you do not have a test kit. That's essential for getting and keeping your pool sparkling.