Double shock and filter nonstop.
Shock the pool with a double dose of chlorine, run the filter 24/7, and brush every surface. That’s the whole plan.
Rainwater dilutes your chlorine and brings in phosphates and organic junk — perfect conditions for algae to bloom. You need to nuke it hard. Use a calcium hypochlorite shock or liquid chlorine at 2x the normal dose for your pool size. Make sure your pH is between 7.2 and 7.4 so the chlorine actually works.
Brush the walls, floor, and steps to break up the algae film. Run the pump continuously until the water clears. Backwash or clean the filter when the pressure goes up — usually after the first day. Don’t bother with algaecide yet unless the algae is super stubborn (green water but no real cloudiness). Skip flocculants until the water is at least partly clear.
It might take two or three days, but it’ll work. Future you will thank yourself when you’re swimming instead of draining.