I have the same problem, but mine is coming from a newly installed sink in the bathroom only from just the cold water. I never had it before from the old faucet, so what is causing the new problem with this? It smells and tastes bad.
In my case one new cold water pipe gave the smell, and here's how it was fixed.
Periodic flushing with water did not help.
Replacing the faucet with a pvc plastic valve didn't help either, so in our case it was the pipe causing the smell.
Apparently the pipe got contaminated during installation and wasn't properly sanitized by the plumber.
I turned off water to the house and disconnected the faucet and the valve to get access to the pipe to sanitize and clean it. This pipe is galvanized iron and is vertical between 1st floor and upstairs attic. After opening I found black particles inside.
Filling the pipe for 4 hours with bleach (8% solution)helped somewhat.
Filling the pipe for 24 hours with bleach (8% solution) and then mechanically cleaning the inside of the pipe with an old toothbrush wet in turpentine and then wicking and drying it off with a paper towel got rid of the smell. Before you try any fluids such as bleach or turpentine, test a section of your pipe (copper, PVC, PEX) for 24 hours to see if bleach will corrode or dissolve it. Make sure to flush all house pipes faucets and showers to make sure all have clean fresh water in them after the treatment.