Early Quenya
súma
noun. nostril
nen
noun. nostril
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 word appearing as ᴱQ. nen “nostril” in several documents from the 1920s (PE14/72; PE15/75; PE16/113). Its plural form nengi made it clear its stem was neng- (PE14/72; PE16/112). Its (Early Qenya) dual nenqi was also “usually used of the nose or both nostrils of one person” (PE15/75).
Conceptual Development: In the Qenya Lexicon of the 1910s, the word for “nostril” was ᴱQ. sūma under the early root ᴱ√SUHYU “breath, exhale”, where its dual sunwi “nostrils” could also be used as “nose” (QL/86). The word súma “nostril” was mentioned in the contemporaneous Poetic and Mythological Words of Eldarissa along with its dual sunwi (PME/86). Under the same early root, Tolkien had ᴱQ. súne as a more ordinary word for “nose”, specifically a nose of a human (QL/86; PME/86). ᴱQ. súne “nose” survived in the documents from the 1920s (PE14/76; PE15/75; PE16/136), but “nostril” became ᴱQ. nen (neng-) as noted above.
See the entry on ᴹQ. nengwe for a discussion of later “nose” words from the 1930s.
Neo-Quenya: Since ᴹ√NEÑ-WI was the base for the word ᴹQ. nengwe “nose” in The Etymologies of the 1930s (Ety/NEÑ-WI), ᴺQ. nen (neng-) “nostril” might remain viable for purposes of Neo-Quenya as a derivative of the shorter form of this root: ᴹ√NEÑ. However, in later Quenya grammar its dual would most likely become ✱nengu, and I would use the dual only for “(pair of) nostrils” and not “nose”.