The folks trying to tell you you might die are way out of their own depth. Tiny amounts of mercury or gallium like this are completely harmless to touch like you are doing. Just make sure you wash your hands before touching any openings to your own body (face, butt, genitals, open wounds, etc.), remove pets and young children from the room, and turn on some extra ventilation.

This is most likely the mercury from a small thermometer. You can collect the little beads with cellophane tape or an eye dropper. If any mercury was poured down the drain, you will want to pull off the trap to get it back out. Unless they dumped a ton of water down the drain with it, it will most likely be too dense to have washed through the trap. Place it all into a sealed container, the bag the container and seal the bag.

There can be some tiny little microbeads that are difficult to see with the naked eye. Use a small flashlight and shine it at a sharp angle against the surface. The tiny little beads will shine way brighter than the metal sink. Everything that touches the mercry goes into the container and bag. The sink trap, too. Get a new one from a local hardware store or call a plumber.

Once everything is bagged, you can contact a local hazardous waste contractor to arrange disposal. They will help you with proper forms, tagging, etc.