One way to interpret this story is to consider the waltz, the dance itself, as an allegory for marriage.

The double voice of the story represents the speaker's social persona and her internal consciousness. Feeling compelled to conform to expectations of femininity and female gender roles, the speaker's social persona is polite, accommodating, and subservient. However, her inner persona reveals her genuine personality, unencumbered by those social expectations. As her inner consciousness is not chained to those social codes and roles, she feels free to rail against those expectations, even to the point of dramatic exaggerations. But, those exaggerations might be more than just hyperbolic reactions to a pressure-filled social situation. Those exaggerations might be metaphoric approximations of what a marriage would be like if the speaker would have to continue to deal with these expectations while containing her true feelings for many years. 

We get the impression that the speaker is a young girl at some dance or, in a modern context, at a club. But as she exaggerates, she can sound like a miserable old woman who's been married for years. 

I hate this creature I'm chained to. I hated him the moment I saw his leering, bestial face. And here I've been locked in his noxious  embrace for the thirty-five years this waltz has lasted. Is that orchestra never going to stop playing? Or must this obscene travesty of a dance go on until hell burns out? 

An allegory is an extended metaphor. As you extend the metaphor here, that the waltz is a metaphor for marriage, other connections emerge. For example, when the speaker refers to being repeatedly kicked in the shin, this could be interpreted as a metaphor for mental or physical abuse, or general disdain for a clumsy dance partner or, following the allegory, an awkward husband/lover. When the waltz is finally over, the speaker says (inner voice) ". . . in my ears there is a silence like the sound of angel voices." Again, following the extended metaphor of the allegory on marriage, this might suggest that she will only find relief with her or his death.