Surprisingly, somewhat related in a circuitous way…
Vomero is a neighborhood in Naples, on top of a hill and directed to upper-middle and higher class. The etymology mix is interesting: its name comes from a villa on there, which has a relation to agriculture, which uses plowshares, aka “vōmer” in Latin… which also was an informal word for penis (then again, what wasn’t in Latin)… but it stuck to the nasal bone with a shape similar to a plow.
“Vomerò” is also the first person singular of the future indicative for the Italian vomere, or “I will vomit” (…not to be confused with the Latin “vomitorium”, although that one’s etymology also comes from vomit)… and arguably, a plowshare is the part that “vomits” earth while plowing.
So you weren’t all that far away: if you vomit, chances are your vomeronasal organ, named after the bone shaped like the tool that vomits while plowing, will get a whiff of whatever goes through.