Yes, fair enough, we did already tell you that the nose was a character in the story… but it's pretty clearly also some kind symbol or allegory or something. A man can't just suddenly develop a sentient nose without it meaning something, can he?
Ok, we're just going to throw it out there—the nose is totally a phallic symbol. And it's not just Shmoop that needs to get its mind out of the gutter. This is a really common interpretation, and don't try to tell us it didn't occur to you! In fact, there's even an edition of the story that takes out the word "nose" altogether and replaces it with just a blank "–––," so readers can just go ahead and throw some other body parts into the mix themselves.
And once you have the whole nose = penis (yeah, we said it) thing in your head, some of the story makes a lot more sense. Check out what happens when Kovalev loses the nose. He's embarrassed to walk around, sure, but what is he really prevented from doing? Hitting on the ladies:
Presently the agreeable swish of ladies' dresses began to be heard. […] a slender maiden in a white frock which outlined delightfully a trim figure […] Kovalev moved a little nearer, pulled up the collar of his shirt, straightened the seals on his gold watch-chain, smiled, and directed special attention towards the slender lady as, swaying like a floweret in spring, she kept raising to her brows a little white hand with fingers almost of transparency. And Kovalev's smiles became broader still when peeping from under the hat he saw there to be an alabaster, rounded little chin, and part of a cheek flushed like an early rose. But all at once he recoiled as though scorched, for all at once he had remembered that he had not a nose on him, but nothing at all. (2.28-29)
Surely you can judge what it is for me meanwhile to be lacking such a conspicuous portion of my frame? […] every Thursday I am due to call upon Madame Chektareva (wife of the State Councilor); whilst Pelagea Grigorievna Podtochina (wife of the Staff-Officer, mother of a pretty daughter) also is one of my closest acquaintances. So, again, judge for yourself how I am situated at present. In such a condition as this I could not possibly present myself before the ladies named. (2.63)
The problem here isn't that they'll think he's deformed. Instead, he's worried about propriety, that the women will see him as less of a man or as not even a man at all. That strikes us as pretty striking evidence.
The clincher, though? When Kovalev gets the nose back, he goes around comparing its size to that of other dudes. He might as well be whipping out a ruler.