Read this and thank me later from saving you from a stupid practice - and find a new vet while you are at it:
http://www.ncbi.nlm.nih.gov/pubmed/19136404
Bottom line, research - no forum bull crap - on ANIMALS shows that:
Vick's Vapor Rub stimulates mucous secretion in test animals. The results of the linked study conclusively showed that Vick's Vapor Rub creates the same inflammatory respiratory reaction that you'd see with an exposure to inhalant irritants. This could lead to mucus obstruction of small airways and increased congestion.
What a brilliant idea - treat a damn RI by irritating the respiratory system and increasing mucous production.
In other words, it does the opposite of what you think it does.
As for eucalyptus oil - inhaling has been linked to vocal cord irritation. Plus, every hippie-dippie site that deals in aromatherapy offers the same warning:
"Topical use or inhalation of eucalyptus oil at low concentrations may be safe, although significant and potentially lethal toxicity has been consistently reported with oral use and may occur with inhalation use as well. All routes of administration should be avoided in children.