First of all, that was not a "small piece of ceramic". I assume you have a Suburban water heater. That "piece of ceramic" was actually pieces of gunk from inside the water heater. Simply flush the water heater with a flush tool that you can get from Camping World. You'll be surprised at how much gunk comes out.
Second - For the lav faucet. Try removing the aerator screen at the end of the faucet and cleaning it out. If that doesn't work, buy a replacement faucet. Get a nice one and you won't have the flow problems you do with you wiz-bang OEM faucet.