What Grit Dog said,
I sanitize my tank each year and drink the water! Yeah, I really do and neither I nor any of my family have had to go to the hospital. Imagine that. There have been a few occasions over my 30 years of camping out of a trailer where we did get a strong sulfur odor. This, I am convinced is from the water we loaded on while away. Once it was so bad we had to go out and buy water but that was the only time.
Use the bleach method to sanitize your system. It is important as others have mentioned that you get this solution in all of the lines. If you have introduced the bad water into your HW tank I suggest you drain it and fill it with the bleach solution too. Get them all, outside shower, spray nozzle at the sink, get them all.
You really can't over do the bleach. If you use a weaker solution you will have to let is sit longer. I use 1 cup in my 30 gallon tank and let is sit for 3 hours or longer.
Good luck. Let us know how you fixed this issue. We all would like to hear.