Your pool has metals, not algae.
Probably. When you add chlorine and your pool goes green instead of clear, that’s usually iron or copper oxidizing. Chlorine is a strong oxidizer — it reacts with dissolved metals in the water, turning them into colored particles that make the pool look like swamp soup.
The fix isn’t more chlorine. That just feeds the reaction. You need a metal sequestrant (a chemical that binds the metals so they can be filtered out) and then let your filter run. If the green is a weird shade — almost blue-green — that’s copper. If it’s a rusty tea color, that’s iron.
Test for metals before dumping in shock. Cheap test strips or a pool store drop-off will tell you. And if you’re on well water, you’re practically guaranteed to have this issue.
Don’t add more chlorine — that makes it worse.