rotten eggs

Recently my family has been fighting a severe head cold.  We have all had our trips to the toilet with diarrea (diarrhea) and also vomiting and just when we start to feel better it comes back.  Now one of my kids is experiencing rotten egg burps and her breath smells of it. She says she feels like she has to vomit but thats as far as it goes. She seems to feel a little better after taking a shower but still can't sleep all the way threw the night.  

I would just like to know what it is that is causing this and what I can do to help her get over it!

thanks