Your story raises many questions and I hope that you will continue to explore them further. It is true that there is some distinction among women in Flatland, although it is not so obvious as it is for men, merely determined by the number of sides. A man might not be able to tell whether where a woman fits into the hierarchy, but a woman might be able to discern things invisible to the masculine eye and mind. Can you devise some ideas that could contribute to such a faculty for discrimination? One key might be sound, a sense not particularly well developed by the males in Flatland, but something that plays a role in various parts of the story, when one creature is mistaken for another because of the sound of the voice. At one point the square cries, "Bass-voiced monstrosity!" and in the visit to Lineland, the sense of hearing is the most acute of all. Another feature is gracefulness of movement, something that can be measured I suppose, and something already noted by A Square as a characteristic of high breeding. But might it be more than that?
This is not to say that the women should become as intolerantly heirarchical as the men, although that might be implied by the idea that women in Flatland can distinguish social class by means other than mere sight. Perhaps the highly developed intuitive faculty can give a clue? The suggestion that women should become more rational (which is not precisely the same as becoming more educated?) might lead to some advantages for society, but not much unless the men become more intuitive at the same time. At least it seems to me that the satire is attacking the disjunction between the Two Cultures, to use a phrase popularized in the 1950's by the academician novelist C. P. Snow, and the remedy for that is for both cultures to give up exclusivity and try to communicate, not just for one to pick up some of the characteristics of the other.
Another book published in 1884 was "The Adventures of Huckleberry Finn". To what extent does the language of "Flatland" embody some of the reactions to the slavery debates? Slavery had been abolished somewhat earlier in England, but not in all of its colonies. Compare the modern American treatments of "The Confessions of Nat Turner" or "The Color Purple".
In class you mentioned Mary Wollstonecraft. How is her work related to your piece? I'm afraid that I don't know it so I can't see where you are playing off her ideas, if you are.
In any case you get the prize for being the first one to place your creative writing on the web page!