Water Has a Rotten Egg Smell At Times
First, wait for a foul-smelling day and obtain samples from before your filter, and from hot and cold faucets. Send them to a testing facility that YOU choose.

Well-established bacteria can easily survive a chlorination treatment, as it will only kill the bacteria on the surface layer.

It might be your city's water. It happens from time to time in my city - just means I can't drink faucet water that day.

If it's in your system, you may need a shock chlorination or acid treatment, or possibly to replace some pipes.

To me, it sounds as though you have well-established sulfur bacteria in your house's pipes.

I would probably spend $20 on bleach before a treatment, just in case. Take out your filters, and using the filter assembly or well cap (if you're in the country), just systematically introduce a couple bottles. Run faucets individually until the bleach mix is coming through all of them. Shut them off, wait 15, run them all for 15, shut them off. Then wait an hour and repeat the process. Then do it again.  Bang on the pipes to shake things up inside - Iron/Sulfur bacteria is literally a sludge layer on the pipes and banging on them is a tried and true method.

In rural WI, where I grew up, when farmers get a foul-smelling hint in their water they pop off the well cap and dump a bottle of bleach down. It's not technically chlorination, but it's cheap and it works.

If the bacteria is in your system and the DIY doesn't work (or you don't feel comfortable doing it), find a good plumber and tell him the situation, including the part about standard chlorination not working. Pipe replacement, shock chlorination, or acid treatment will be the next step.

Good luck.