The only time I had egg smell from the hot water. I turned the water pump off Drained the hot water tank. Funnel poured some bleach into the drain hole. Put the drain plug back in. Turned on the water pump. Opened the relief valve till water came out. Shut off water pump. Waited 24 hours and then drained the tank. Ran the pump a bit to flush the bottom of the tank. Turned pump off. Put drain plug back in. Turned on the water pump. Turned on the hot water tap in the kitchen and waited for water to come out of it, done.
Oh it had a slight chlorine smell at first. About the same as when you finish de-winterizing just the pipes. The smell never came back.