If your well is drilled and designed in a way that lets surface water get in, it should not be used for a drinking water supply unless there is a really good treatment being used as well. The nitrate and ferts from farming are among the least harmful things found in surface water. Animal and human waste are often in surface water. Any number of diseases are found. Is your well tested and approved for drinking water? If it is not and you see changes after rains, I would not drink or cook with it.
It is correct to assume that any good water treatment will increase the amount of chlorine or chloramine added if they are drawing from a surface source like a lake. Since these chemicals react with the organics and pollution in the water, the amount of chemical added at the treatment plant has to be increased as the pollution increases. When you get a heavy rain everything that is left on the street or your yard is being washed into the lake. That is everything from hog lots and dead cats to the vomit from the gutter! Oil dripping from your car and the pesticide used last week go in there, too. OOOW!
I hope they add a bit more chemical to treat that stuff!
But that doesn't mean the water you get at the faucet becomes dangerous. The whole point of water treatment is to make the water safe to drink so there are limits and testing that go with delivering the water. There are test sites all around the system which show how much chemical is left by the time it arrives at your house. (3-10 PPM)
If there is so much debris washed into the water like if you are drinking out of the Mississippi River after a flood that they can't get it safe with chemicals within the allowed amount, they have to add extra filters and other treatment methods.
The other choice is all the disease that is rampant in countries that don't have water treatment available. Anybody like to have a good case of typhus ?