I would suspect that you are seeing the results of a increase in pressure, by code the water pressure in your home needs to be less than 80 psi.
High pressure is controlled by a Pressure Reducing Valve (PRV) when needed you may have one that has failed or, not have one installed and need one.
Additionally sometimes a closed system is created by a check valve or, PRV and measures to control thermal expansion from the water heater heating cold water must be used. These measures would include a thermal expansion tank or in some areas of the country Mid-Atlantic in particular relief valves are used. If you have one of these devices it may have failed.
Expansion from a run away water heater is very unusual as several safety devices would have had to fail mainly the Thermostat, ECO, and T&P Valve, also you would have probably noticed the extremely hot water.
In any case I would use a pressure gage to check the pressure and troubleshoot the problem if high pressure is noted.
The faucets will also need to be repaired with either a new cartridge or, new washers and seats depending on the brand and model faucets you have.