In this my waiting

[dukealien]

In this my waiting

Ah, in this my waiting,  another comma after "this?"  Probably not.
how fast October goes,
how swiftly day fades into dark.  nice stanza.

My melancholic rose,
like one who sailed an ancient river
where the green papyrus grows -  could replace "the" with further one-syllable description but, really, stet.  Reads well.

like her, like you: no age can wither,  
nor custom stale. Your nose  sophisticated reference back to Shakespear's Cleopatra, stopping short of "variety"
may be substantially shorter,  humor noted, kind of a Thurber multisyllable with "substantially"
but there’s poetry in your prose.  and then return to serious compliment.

In moderate critique, the stage-setting first stanza is pleasant but doesn't set it for what follows.  Speaker is sad, but this is only implied.

In S2, who's melancholic?  From S1, the speaker but, proximately, the beloved.  Not sure about that ambiguity, but it's not a serious problem.

In S3, I envy the speaker his well-read beloved who will catch the dramatic reference.  And will take the compliment to her nose - as being less outstanding than Cleopatra's - in the spirit intended despite definite levity.  Which is to say, she's a good sport.

I have no real advice on improvement, other than (maybe) to make clear that the speaker rather than the beloved is suffering melancholy.  Making the nose size comparison less funny does not appeal:  it's a short poem, it has turns, and it ends up where intended.  Good job.  And may *your* Cleo be no less appreciative.