A rotten-egg smell has several possible sources, and they do not all need the same fix. Some come from the water itself, some from the water heater, and some from the drain. Sort the cause first, and the treatment choice gets much simpler.
Start with the pattern
Run the cold tap for a minute, then the hot tap for a minute. Smell each one in a clean glass in daylight. Note whether the smell is in both taps, only the hot tap, or only at the drain. A smell only on the hot side points toward the water heater rather than the incoming supply. A smell in both taps points toward the water source, which is where treatment decisions usually start.
Separate the glass from the drain
Smell the drain separately. A sewer-gas odor often comes from a dry trap, a cracked vent, or a drain that has not been run for a while. Pour water down the drain to refill the trap, wait, and smell again. If the drain smell goes away but the glass still smells, the problem is in the water.
Look at the water heater
Hot-only sulfur smells are often linked to the water heater, where bacteria and certain anode rod materials can produce hydrogen sulfide. Ask whoever services the heater what type of anode rod is installed and when it was last checked. Do not assume the heater is the cause until the cold side has been ruled out.
Ask what a test should report
If the cold tap also smells, ask a testing lab to report hydrogen sulfide, iron, manganese, and bacteria results along with the usual water chemistry. A test that does not name these items may miss the cause. Before you compare treatment options, check what each option is designed to remove, because aeration, oxidizing filters, carbon, and disinfection work on different parts of the problem.
Decide what to do next
If the cold water is clean and only the hot tap smells, the next step is usually the water heater, not a whole-house system. If both taps smell, the water needs testing before any equipment is chosen. Either way, write down which tap smelled, when it started, and what you tried, so the person you call starts from facts instead of guesses.