Stinky water from ONLY one faucet.

dannat

We are only a well water system in rural Texas that is approx 10 yrs old. The house and fixtures are about 2 yrs old. I have read on here why why water has rotten egg/sulphur smell, but can someone help me and tell me why it only occurs in _ one single faucet __ and no others? Cold water faucet in bathroom sink runs stinky for about 30 seconds. Thanks for any help. I can figures most plumbing problems but this one has me stumped.