My dog has an issue with her tear duct and mucus glands on the right side, cause her to often have her right nostril clogged by dried mucus. When discussing this with her vet I want to use a more clinical term than “booger.” (I’ve been saying "clogged with dried mucus, but if there is a more expedient way of saying it, I’d like to know.)
Nose candy?
Dehydrolyzed Phlegm Accretion
I’ve heard a booger described as a slang term for “dried nasal mucus.” So you could say dried nasal mucus.
“Dried snot” will impress the vet.
This has been asked here several times with no definitive answer, but at least a few better options than “booger” for your vet visit.
I did not look through the prior threads, but the most typical ‘medical’ term for dried mucus is “inspissated mucus.”
However most of us would still just say, “dried mucus.”
From wikipedia:
Dried nasal mucus, pieces of which are colloquially known as boogies[1] or boogers,[2] or bogeys is found in the nose and is a result of drying of the normally viscous colloidal mucus (or snot).[3]
So we’ll go with the cumbersome dried nasal mucus 
Just say “bogey” (or “booger”), your Vet won’t be unaware of the term and you will both know EXACTLY what you are talking about.
Trust me, when the Vet goes home and his snot-nosed kids greet him, he doesn’t tell them they have “nasal mucus” over their faces, he grabs a tissue and says “Urgh, c’mere snotty, clean-up time”
One thing a lot of people don’t appreciate about technical terminology is that its purpose isn’t to make the users sound smart or as a shibboleth to separate the professionals from layfolk (though unfortunately it’s often used for those purpose)-- The purpose of technical terminology is to be clear and precise. The term “booger” is unambiguous and universally understood, and so serves just fine for describing those objects.
Oh! DNMs!!