You ( and Watermom of course ) are right. Is the algae in the water or on the walls and floor? Brushing the pool will help get the chlorine to the algae stuck on pool surfaces.
So, the recipie is:
Bring your FC up to shock level for your CYA and keep it there as best as you can by testing and dosing as often as you can.
Shut off the SWCG and run the pump 24/7.
Backwash the filter when pressure climbs 8-10psi over clean pressure.
Brush the pool, especially where algae is visible.
When you have less than 1 ppm FC loss overnight and minimal CC (less than 0.5 if using the 10ml sample size), keep the FC at shock for one more day.
Please use the "Edit your signature" link in Watermom's sig to add your pool's particulars to your signature.

Be patient.
Don't worry, you'll get this under control.
Keep us up to date.