My first language is Finnish, which has a very straightforward correspondence between spelling and pronunciation.

I would divide the drug names into four categories based on how they sound:

Obviously a substance: Amantidine, Sildenafil

Generic fantasy names / pronounceable strings with no meaning: Azafen, Clédial, Cymbalta, Desyrel, Edronax, Luvox

Could be Tolkienian, but it's spelled wrong: Sintamil

Could be Tolkienian, but the final syllable is wrong: Elronon, Eskalith, Nardil

Additionally, the two Tolkien characters I had to guess were both kings of Gondor: Minalcar and Narmacil. Their names are in Quenya, while the commonly used names for elves etc. are in Sindarin, which sounds different.

It sounds like you got by more on thorough knowledge of Tolkien than your knowledge of Finnish. I'm going to guess there's more speakers of non-English languages here than of Quenya and Sindarin (which may have been pharmaceutical names for all I know).