Should I shock my pool right after it rains?

Yes, but you need to do it right. Rain dilutes chlorine, muddies the water, and can drop your pH. So before you dump in a bag of shock, grab a test kit and adjust pH to 7.2–7.4 first — shock works best there. Use a non-stabilized chlorine like calcium hypochlorite, and double the dose if the water looks cloudy or you had a big storm. Run the pump overnight and brush the walls the next morning.