Could be a number of things... Duvel is my favorite beer and can't say that I have tasted a medicinal taste. My taste buds may be different than yours though... Here's a quote from the BJCP Guidelines regarding this type of beer:
"Flavor: Complex with significant fruity esters, moderate spiciness and low to moderate alcohol and hop aromas. Esters are reminiscent of lighter fruits such as pears, oranges or apples. Moderate spicy, peppery phenols. A lot to moderate yet distinctive perfumy, floral hop character is often present. Alcohols are soft, spicy, perfumy and low-to-moderate in intensity. No hot alcohol or solventy aromas. The malt character is light. No diacetyl."
The medicinal flavors you are tasting may be coming from the phenols, esters, or even the alcohol. Just thought this would help kinda narrow it down for you.
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