It's impossible to tell without accurate test results, plus pictures, but here's what I *think* is going on.

1. You've killed all, or most of the algae, turning the cloudy green into cloudy white. BUT, if you don't get some bleach in there RIGHT away, you'll do a RESET, regrowing all that algae, and being EXACTLY where you were before. Put 1/4 gallon of bleach in THIS evening. Do it again, TOMORROW evening, but then brush the pool completely. There may be hidden piles of algae in the pool, and you do NOT want them stirred up while the chlorine is low. After brushing, if there's the slightest evidence that the water changed to greenish -- add 2 cups MORE bleach.

2. I'm not sure what HTH shock you have, but most types of HTH shock contain calcium hypochlorite. It's quite possible, with this form of chlorine, to fill your pool with milky looking calcium carbonate. But, without test results, I can't do more than guess.

3. Intex filter cartridges aren't very good, and don't last very long. Intex suggests replacing them every two 2 weeks. They do work well enough to keep a pool clear IF nothing goes wrong. But when a pool gets cloudy, they filter out the cloud, very, very slowly.

Without new Unicel cartridges and some polyquat . . . it may take the rest of the summer to get your pool clear.

Honestly, if your water isn't very expensive, it would be easier to refill and start over.

Sorry.