If you have staining at the bottom of the bowel, you need to go see a doctor.
Sorry, couldn't resist.
As to your specific system problem,
Get a real water test. The GE whole house "filters" are just simple, small carbon tanks that are usually 1/3 the size they should be. Running bleach through an iron fouled softener can really make the iron stick to the resin, making cleaning with a mild acid pointless.
Many counties require a water test be performed on a well prior to closing escrow. It is kind of a good idea to test the water at least every couple years, annually is preferred. it is fairly inexpensive, and very important considering you are drinking, bathing, and breathing the water.