Iron staining plus rotten-egg odor often points toward a whole-house oxidation and regenerating-media system designed for both iron and hydrogen sulfide.
If both hot and cold water smell and testing confirms iron/sulfur chemistry, a dedicated whole-house oxidation/filter system is the right category. If the odor is only in hot water, inspect the water heater before buying whole-house equipment.
Air-injection and similar oxidation systems convert dissolved iron and hydrogen sulfide into forms that can be captured by media. The same platform can often address manganese as well when the measured levels fit the manufacturer's treatment range.
Relevant when testing confirms iron, sulfur and/or manganese within the system's treatment range.
A rotten-egg smell only in hot water can come from the heater environment or anode rod. Confirm whether cold water smells before investing in a whole-house sulfur system.
Diagnose hot-water-only sulfur odor →
The filter must support household service flow and also receive enough backwash flow from the well pump. A system can be chemically correct yet perform poorly if the pump cannot clean the media bed.
Iron, manganese, hydrogen sulfide indicators, pH and hardness should all be reviewed together. High hardness may justify adding a softener downstream after iron/sulfur treatment.