Do you mean the smell of your stool? or the smell of your skin/sweat?
Nearly all "sulfur smell" comes from the microbiome--the sulfur-containing amino acids that make up part of our own cells don't smell strongly like sulfur, that requires that bacteria break them down into smaller, volatile compounds.
There are many sulfur amino acid-degrading (e.g. many Clostridia) and sulfate reducing (produce sulfur smell from sulfate, which is an odorless form of sulfur), e.g. Desufovibrio and Bilophila, bacteria that can live in the gut. The most common cause of sulfur-, onion-, or grapefruit-smelling sweat is corynebacteria living on the skin, but it's definitely possible that some sulfur compounds from the gut are absorbed and sweated out as well (many people smell of garlic after eating it).
It's likely that the Bactrim killed off some bacteria that were generating volatile sulfur compounds. I haven't noticed my sweat/skin odor depending significantly on my gut, however the taste/smell in my own mouth, particularly after eating, DOES depend greatly on my gut health, as of course does the smell of my stool.
