Shock harder than you think
Yes, but you need to keep the chlorine level high until it holds.
The mistake most people make is shocking once and walking away. Algae blooms laugh at that. You need to super-chlorinate to the shock level based on your cyanuric acid (CYA) level — not a generic “one gallon per 10,000 gallons” guess. Look up a CYA/chlorine chart. Then raise it to shock level and keep it there for at least 24 hours, ideally until the water clears and combined chlorine is zero.
Brush every surface you can reach while the pump runs 24/7. Vacuum to waste if you can. Backwash or clean your filter once the pressure rises. Algae is dead when it turns white or gray, when it stops coming back after brushing.
The only way to prevent recurrence is to make sure every last bit is dead, and to keep your normal chlorine level consistent going forward. Also, if you have phosphates, consider a phosphate remover — but that’s a secondary step.
Don’t stop early. That’s how you get to do this all over again next month.