I would think you need to install a filter to remove the sulfur odor. Do you have that same smell out of the tap? Does your fridge have its own filter? Most do, perhaps it is time to change it out. The charcoal filter used should remove this offensive odor. IF its happening from faucets, then it may be time to have the water checked. AS water tables move up and down with the crazy weather were having so does the water quality change. A low cost water check will solve a whole host of issues if your having them by answering exactly what the water quality it is that you have coming out of the tap.
I have already changed the filter and the odor is not in the filter nor coming from the faucet. Very strange.
Judy, A few things can cause this odor, One which is doubtful is if the water connection is on the hot water side of your plumbing the anode rod which protects the hot water heater has been known to cause this smell on occasion when its nearing its end of life.
Is your area known for sulfur water? What about the rest of the house? Is the smell coming out of any of them? What about the shower when its used?
The only other think I would think of is the tubing used in the fridge, perhaps it has deteriorated because of age and require replacement.