Hey! Glad to hear there is progress!

If you really want it to clear up more quickly, do as advised here and test and add chlorine a few times a day and leave the pump running 24/7 until you conquer the beast

Brushing the pool is GREAT! - it gets the chlorine into the 'low interface' areas and stirs up any algae that is still trying to keep it's hold.

How high is the sand in your filter - it should be ~ 1/2 way full - the filter needs a certain amount of 'head room' to filter properly, if it had been overfilled in the past, that could explain why some is coming out when you backwash.