Rotten-egg smell: filter, disinfect the well, or both
A rotten-egg smell is a reason to test, not a result. The same odor can come from the groundwater, from iron bacteria, or from the water heater. Those three do not get the same fix.
Updated
A house that smells like rotten eggs sends people straight to a filter catalog. Sometimes a filter is the right conversation. Sometimes the smell is the water heater. Sometimes the well needs disinfection before any tank goes in the basement. Smell alone does not tell you which one.
The gas people mean
Hydrogen sulfide is the usual source of a rotten-egg smell in well water. It is a gas. It can be in the groundwater, it can be produced by bacteria that live on sulfate, and it can be produced inside a water heater. EPA's secondary standards do not list a hydrogen sulfide limit in milligrams per liter. They list an odor guideline of 3 threshold odor number, and they name a rotten-egg smell as one example of odor, next to musty and chemical smells. So the complaint is real, and it is still not a number you can size a tank from.
If odor is why you are testing, ask the lab for its sulfide method before you draw the sample. The gas can leave an open bottle. "None detected" on a casually filled jug is not the same as "this water does not smell." The rest of the report still matters. Use how to read a well-water lab report for the iron, manganese, pH, and health lines that ride along with the odor.
Hot water only, or every cold tap
Run a cold tap that is far from the water heater until the water is as cold as it gets. Smell it. Then run the hot water and smell that.
Only the hot side smells
The heater is a prime suspect. A magnesium anode rod is there to corrode in place of the steel tank. In some water that reaction produces hydrogen sulfide inside the heater, so the rotten-egg smell shows up when you draw hot water and not when you draw cold. That is a heater problem. A whole-house iron filter on the cold main will not be the thing that fixes it.
Do not pull the anode out to test the theory. The rod is what slows the tank rusting through. A plumber can check it, sometimes by replacing a magnesium rod with a different anode the heater manufacturer allows, or by dealing with sludge that has already collected in the tank. Those are plumbing decisions, with corrosion on one side of the ledger and odor on the other.
The cold side smells too
Then the gas is in the well or the building's cold plumbing, not only in the heater. Changing the anode will not fix the cold water. A filter may belong in the plan, after a lab report, and after you have looked at the health lines. The first burst of hot water can smell worse than the cold even in this case, because the heater stores water long enough for the odor to build. Cold-water odor is the clue that the well is involved.
Iron bacteria can smell bad without a huge iron number
Some wells grow iron bacteria and other slime-formers. Clues are a rusty or oily film, stringy growth in the toilet tank, and a smell that is rotten, swampy, or musty. Dissolved iron on the lab report can look modest, because the biology is the story rather than a high dissolved-metal number.
Iron bacteria are not the same result as total coliform or E. coli. Coliform and E. coli are health warnings. They can mean the well is open to waste or surface water. Iron bacteria are a nuisance that ruins plumbing and filter media. Neither result is a reason to buy a bigger iron tank and hope. CDC's well safety guidance says not to drink water that is or may be contaminated with harmful germs, and to call the health department.
When a filter is the usual conversation
Cold water smells, the lab does not show a health contaminant, iron bacteria are absent or have already been dealt with, and a manufacturer publishes a hydrogen sulfide limit that your result does not exceed. Then an oxidation filter is the equipment people buy. Air injection or a peroxide feed are the two categories. Match the sulfide limit, the iron limit, the manganese limit, the pH, and the flow. Air injection versus peroxide versus a softener is the difference. SpringWell, US Water Systems, and SoftPro are the three brand pages to interrogate with the same questions, not three winners.
When disinfection comes before the catalog
A filter treats water passing through it today. It does not scrub a casing full of slime, and a fresh media bed can become another habitat. If an iron-bacteria test is positive, or the well has a coliform or E. coli hit, talk to your health department or a licensed well contractor about disinfecting the well before you buy a tank.
Disinfecting a well is sometimes called shocking it. It uses a concentrated chlorine product. The amount depends on the depth and diameter of that well, the volume of the plumbing, and the rules in your state. Get it wrong and you can damage equipment, miss the organisms you meant to kill, or handle a chemical you did not need to measure out.
This site will not tell you how
We do not print bleach doses, concentrations, contact times, or a step-by-step for shocking a well. Your state health department or your county cooperative extension is the office that publishes the procedure for wells where you live. A licensed well contractor can do the work. Afterward, retest with a certified lab. Do not install a filter and skip the new bacteria test because the smell faded for a week.
EPA's private-well site and your health department are the starting points. Do not follow a dose you found in a comment thread.
Sometimes the honest answer is both
Disinfect and retest when bacteria are part of the result. If hydrogen sulfide, iron, or manganese is still on the new report once the bacteriological problem is resolved, size a filter from that later sheet. Buying the tank first, then sending a shock treatment through a brand-new bed, is a common way to ruin media.
If the smell is only in the hot water, fix the heater question first. You may not need a whole-house filter at all.
What the smell does not prove
A strong rotten-egg smell is not proof of E. coli. A faint smell is not proof the water is fine to drink. Smell is a reason to test. If anyone in the house is sick, or the water changed suddenly after a flood, a new pump, or work on the casing, stop using it for drinking and cooking and call the health department. Do not wait on a freight shipment.