you city water ,they added chlorine to the water for the same reason , you need to bleach(chlorine) your well. wouldn't even hurt to do it two time a year.
I shock my well once a year. 4 gal. of bleach down the well .run thru all area of the house , till you smell the bleach. Let set a few hours , then run all fixture , don't forget the washer. Till the bleach smell is gone.
Big mistake i made, i forgot to flush the washer......my first load...