Test and shock is usually all you need.
Yes, but keep it simple. Heavy rain dilutes your chemicals and can bring in dirt or algae spores. You don’t need a full rebalance—just test and adjust.
Check pH first. Rain tends to lower it (acidic), so you’ll probably need a little soda ash or borax to bring it back to 7.4–7.6. Then check chlorine—rain can wash out stabilizer and kill your residual. Shock it hard (double your normal dose) to kill anything that blew in.
Alkalinity and calcium hardly budge from one storm, so skip testing those unless you’re paranoid. Skim debris, run the pump for a few hours, and you’re fine.
Most “heavy rain problems” fix themselves with a good shock and a skim.