"I'm not real? That's just what them liberal schools want you to believe" - Dracula, as quoted on the Internet.
Garlic in cloves is pretty agreeable, but that is not how we use them. We chop it up, which releases the allinase enzyme and that converts generally agreeable alliin molecules into smelly allicin. Epidemiologists tout garlic for everything from killing fungi to preventing cancer and say it is due to allicin. But it breaks down fast and creates a bunch of other stinky sulfur compounds, the most persistent of which is allyl methyl sulfide. That one is going to stick around, it is going in your bloodstream and it is going into your lungs - which leads to that bad odor when you sweat or even breathe.
What does that have to do with vampires? Not much, but Vampire Hunters swear by garlic ever since Van Helsing wrapped her neck in it in Bram Stoker's "Dracula"(1) and if it's in their blood, you'll be the one bit by the stench.
Except science is on your side, so have a little Faith.
Elisha Dushku was Faith in the "Buffy The Vampire TV show. See what I did there? Aren't I clever?
Lots of remedies for garlic are touted by folk medicine, but are you going to gargle baking soda? Do you have a Wiccan on standby who has fresh mint leaves laying around? Of course not - but you do probably have milk and chewing gum, and science shows those can be effective. Milk may not make sense, but there is a chemistry reason hot wings eaters swear by it also, while gum is more intuitive. It generates saliva, which speeds up the biological process that gets rid of the odor.
It's worth a try. Anything is better than rinsing with lemon or chewing on rosemary for a day.
(1) Not entirely made up. Vampires had been in folk lore for a long time. People assumed they were real and that it was a disease of the blood, and that garlic was a natural remedy for diseases. The Victorian era had an obsession with disease - this was decades before penicillin - so Stoker was just building on tales that were popular.