6 gallons of bleach a day is not going to be enough to maintain shock level. You need to bring the pool back up to shock level more than once a day, preferably several times a day, if you want to get ahead of the algae.
How did you test the CYA? Is that your test result or the pool store test result?
Even with backwashing, you have added enough to get to about 40 CYA and just doesn't seem like it could be 10. Not to mention, 10 would be very hard to test.
Suggestions: First lower your pH to around 7.2 to 7.4ish.
You have to continue to shock maintaining shock level and increasing FC to shock level as often as possible and at least TWICE per day and at least once in the evening.
Can you post a pic?
What is the name of the bags of shock (ingredients) that you used last night?
Is the only issue green algae water or is there debris in the pool on the bottom? Leaves & junk?
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