Unless you diluted the stabilizer in very hot water - you will likely need to wait a while to get any effect from it. Stabilizer (grainular) takes a long time to dissolve (a few days if you poured it into your skimmer)

Also - if you added the stabilizer to the skimmer - be sure to NOT backwash for a few days, or you'll be backwashing the undissolved grainular stabilizer out of the filter.

Keep your Cl level high for a while, and run your filter 24 hours a day until the water is clear. It will take a few days to filter out all the dead algae. I'm assuming your 'cloudiness' is not a dark green cloudiness, but rather a whitish color. If it's whitish (maybe very light blue, or very light green tinted) then you have killed the algae, and now just need to filter it out.

The only quick fix is a clarifier or flock treatment for your water to help the dead algae settle to the bottom to be vacuumed out - however I don't recommend it - the filter will get it all in a matter of a few days.