I know it's not a folk song, but Miss Adelaide's Lament (from Guys and Dolls) is perfect for med students.  Miss Adelaide (Sky Masterson's moll) keeps reading medical textbook descriptions of "post nasal drip" and other sinus cavity ailments and their relation to socio-emotional issues.  Each verse of these descriptions ends with

"in other words, ...
a person can develop a cold."

Then there's another non-folk one that's relevant:
"Doctor, Doctor, gimme the news

I gotta bad case o' lovin' you!"