Early Quenya
qáme
noun. sickness, nausea
leume
noun. sickness
qama-
verb. to be ill, vomit
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 verb appearing as ᴱQ. qama- “am ill; vomit” in the Qenya Lexicon of the 1910s under the early root ᴱ√QAMA (QL/76).
Neo-Quenya: I’d retain ᴺQ. quam- “to be ill, vomit” for purposes of Neo-Quenya, especially since ᴹ√KWAM continued to be associated with sickness in Tolkien’s later writings (Ety/KWAM).