You don't need to chlorinate water from your own well, unless maybe you have a cistern that you are filling for storage.

And who's going to know if you are drinking it or watering your garden?

At the very least I would UV disinfect anything coming from the ground and absolutely make use of a 20 micron sediment filter if only to address cognitive load: Another place, another time, coliform bacteria from the well. Super fun(not).