Black greasy specks in sinks, dishwasher, etc. at home
Water heater anodes usually last about 3 to 5 years or so depending on the chemistry and hardness of your water, so chances are, if your water heater is only 3 years old, that's not the problem. That being said, it wouldn't hurt to take a peek at the anode and make sure it's doing OK.

The top of the anode rod is typically visible on the top of your water heater. It will look kind of like a bolt head on the top of the heater. You should be able to loosen it with a wrench and extract the anode to inspect it and replace it. If you don't see one of those on the top of the heater, the anode might be integrated with the hot water outlet pipe. You can disconnect the pipe and extract the anode that way.



From what I know, magnesium anode rods have a "bump" in the center of the cover nut while aluminum/zinc rods have smooth-faced nuts. I don't know if this is a "universal thing" or it varies from manufacturer to manufacturer, but that has been my experience.

Aluminum:



Magnesium:



Most water heaters have aluminum anodes installed by default from the factory, but it sounds like you may have a magnesium rod and high sulfates in your water. That combination can cause hydrogen sulfides to form as the anode reacts with the water and produces black, oily particles to settle inside the water tank and float through the plumbing in one degree or another.

You might be able to get rid of the black specks by draining or flushing out your water heater (there should be a drain tap a the bottom of the tank that you can hook a garden hose up to) and replacing your magnesium anode with an aluminum or aluminum/zinc anode rod.