Here's a article I found on putting bleach in your house water.
The Problem With Chlorine Bleach
First thing to do is to avoid putting bleach into the cistern. (Read more on this subject at the chlorine page.)
In a cistern's water, and notably in the sediment at the bottom of the decanting basin, lots of bacteria – mostly harmless – thrive, conveying to the water a biological equilibrium that varies from season to season. Like the wine in a barrel, the cistern's water «lives» and changes with the seasons. Introducing a biocide like bleach gravely perturbs this equilibrium. The chlorine found in bleach indiscriminately kills all bacteria, which then break up, discharging their genetic matter into the water. The medium becomes oxidant, thus favouring the advent of bacteriophagic viruses that feed on the destroyed bacteria's genetic matter. Unless one resorts to reverse osmosis for drinking water, these viruses will not be adequately filtered and may end up in the drinking water. Once absorbed into our body, these viruses can mutate and produce pathogenic strains. The water having become oxidant because of the chlorine makes matters worse by decreasing the electronic activity of the liquids within our body. Generally, the chlorine weakens our immune system, as much by ingestion as from external use. Infants and young children are particularly sensitive to chlorine. After having switched over from city water to rainwater, many families have observed a reduction, and even the elimination of allergies.
For an infant, the daily bath in chlorinated water is far from beneficial You can mitigate this by placing an activated carbon filter placed upstream from the faucet that provides an infant's bath water.
What type of system do you have? A open one where the water is sprayed into a holding tank from above or closed tank with impellers and forced air?
Sometimes when I water the plants straight from the well I get a big pop of air .
Could ne your pump's cavatating (sucking air) What type pump do you Have? A submersible or a surface pump?
The well pump shouldn't affect the house. You have a separate pump from the tank to the house.
Back to you, Tom