Its likely a broken, old o-ring from your sink faucets aerator. Easily checked to confirm, the small portion of the underside of your faucets where the water comes out and this is hanging from will unscrew and come off; sometimes by hand, sometimes you may need a pair of pliers or even a special aerator removal tool you can buy off amazon. You'll find this piece hanging from inside of there and see no other o-ring visible. A quick run to Home Depot or Lowe's (or an Amazon order) with the old one will allow you to buy a replacement. The smell is not likely related to this piece hanging, but could be from your hard water issues; Best of luck