A partially plugged cat could possibly cause the problem you're having .With regard to the egg smell ,many causes , such as
" Rotten Eggs
The smell of rotten eggs is due to a compound called hydrogen sulfide. This comes from the small amount of sulfur that is present in the fuel. Normally the sulfur is converted to sulfur dioxide, which has no odor. When the converter breaks or the filtering layers have worn down inside the converter, the sulfur is not transformed into the odorless form. Therefore a strong rotten egg smell is produced. Another possible cause for this smell may be that the converter is plugged. Unfortunately you cannot repair a converter but need to have it completely replaced. Two other causes of rotten eggs besides a broken catalytic converter include an engine that is running too hot or a broken fuel pressure regulator. You can easily deal with the fuel pressure regulator by replacing the fuel filter."