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.
nin
noun. nose, beak
ni
pronoun. I, me
man táre antáva nin ilúvatar, ilúvatar?
what will the Father, O Father, give me
nengwe
noun. nose
nye
pronoun. me, I
nén
noun. water
-nye
suffix. I
parka ëan Archaic
I am thirsty
parka ëa nyé
I am thirsty
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 for “nose” in The Etymologies written around 1937, derived from ᴹ√NEÑ-WI (Ety/NEÑ-WI), an elaboration of the shorter root ᴹ√NEÑ (EtyAC/NEÑ-WI). Given its primitive form, its stem ought to be nengwi-, but in attested compounds this word is consistently nengwe-, so perhaps Tolkien changed his mind on its primitive form.
Conceptual Development: The earliest percursor to this word seems to be ᴱQ. nen (neng-) “nostril” in several documents from the 1920s (PE14/72; PE15/75; PE16/113), whose dual nenqi was also used for a “nose” of one person (PE14/76; PE15/75). In the Declension of Nouns from the early 1930s, Tolkien had nin (ning-) “beak, nose” < ᴹ✶nengǝ (PE21/26), though this phonetic shift of short e to i is rather unusual and seems to be limited to this document.