Whole house chlorinator??

We live in the country on well water. Our well water has iron bacteria in it and we hate how our clothes smell after washing them for so long and then when you sweat in them, there is a horrendous yucky smell that emits from them. Very musty and just yuck. We won't even drink the water from there because we dislike the taste...not really bad, but we know it has iron bacteria so I think its mind over matter. I do cook with it and shower with it. We have a whole house water softener that has been wonderful over the years. My question is, if we install a whole house chlorinator, is there one that is better than another? Want something affordable. Also, will we need to install a carbon filter as well? This is the one I was looking at purchasing to have installed. Just wondered if they work really well and kill the iron bacteria so hopefully we could at least have great smelling clean clothes again like when we lived in town and had city water.
https://www.cleanwaterstore.com/chl...rVKvqGHsTG6xa7ASv5mqQ2lFIM1RiH6BoC3YwQAvD_BwE

When adding chlorine you need enough contact time for it to work. Usually that means adding a retention tank or larger pressure tank. However, many people use a pellet chlorinator that drops pellets down the well. This treats the problem at the source and gives plenty of retention time. Other people will just routinely shock the well with chlorine.

You probably have iron bacteria which is ferrous (slime). You need to oxygenate it so it can become ferrous so that it can become ferric (solid) and filtered out. You need an iron filter to do that.