Is my well water supposed to smell like rotten eggs?
It is not at all unusual for well water to have a sulfur content. To rule out the water softener, give it a complete clean out then check your book or with the manufacturer to see what the proper setting is. If all that does not change anything then, likely, you just have a very high mineral content in your water. A good filtration system will solve that but if money is tight… Anyway do this test on your system and go from there. I think I would price a good diatenacious earth filter system and start saving!