I am suspecting something is growing. I am not a pro. What I think I would do may not be what you should do.
I would sanitize my plumbing, but you also want to minimize the chlorine going into the septic. Not sure how you would handle that. The septic can handle some bleach. I think what I would do for that shower, because of the high volume that might be involved, would be to spray water into the/a tub, and use a pump to pump, via a hose, to outside drainage. I already have the utility pump and hoses. If I did not, I might just keep the spray with the chlorine water brief. Not sure.
You might do that as part of sanitizing your well and the rest of your plumbing including the water heater. I figure to do that every couple years.
http://www.moravecwaterwells.com/index.php/maintainance/disinfection-and-testing is my favorite procedure for the well, and then I follow by feeding that chlorinated water in the well to the house after letting the chlorine levels drop. I got some high-range chlorine strips and some fairly narrow range pH paper to help.
For just the shower, you could maybe introduce chlorine into your whole-house filter housing.
It could even be that you could crank up the heat on the WH, if you don't have a mixing valve, and running the extra-hot water through the shower head for a while. I don't know if that would be effective.