Middle Primitive Elvish
slaiwā
adjective. sickly, sick, ill
gengwa
root. sick
There are more words but they are from Tolkien's earlier conceptional periods. Tolkien likely changed these words as he evolved the aesthetics and completeness of the languages. You may even find languages that Tolkien later rejected. Do not mix words from different time periods unless you are familiar with the phonetic developments.
Below: Tolkien's Late Period (1950–1973). These are from Tolkien's late conceptual period — his most settled forms of the languages. Prefer these over the earlier ones above when composing new text.
A root in The Etymologies of the 1930s glossed “sick” with derivatives ᴹQ. engwa/N. gem “sickly” (Ety/GENG-WĀ). It was given as ᴹ√GENG-WĀ, and thus represented an extension of an otherwise unattested root ᴹ√GENG. In the entry for ᴹ√YEN from The Etymologies it appeared as ᴹ√GEM in the discussion of N. ingem “old, (lit.) year-sick” (EtyAC/YEN), but I believe this represents the Noldorin phonetic developments of the true primitive form rather than a conceptual variation. The continued appearance of Q. Engwar in The Silmarillion narratives of the 1950s and 60s hints that this root may have remained valid as well.