Shkoyach DY! So it’s pretty clear that according to both the Shulchan Aruch and the Rema, women have no chiyuv to get married.
I just read the Aruch HaShulchan on the topic (Even HaEzer, 1/1-3). He explains the whole inyan, and it was very interesting.
His basic points are:
1. Women are not obligated in “Pru u’rvu” and can choose to remain single.
2. When Noach left the Taivah, the women may have had been obligated in the Mitzvah because at that point, the men couldn’t have fulfilled the Mitzvah w/o them, but this is not true of later generations.
3. Getting married to avoid “chashad” is an “aitza tova” (good idea), but not an obligation.
4. Whether or not “chashad” applies depends on the particular place. It is never an obligation, and it doesn’t even necessarily apply in all places (I would think that it doesn’t apply nowadays at all – I have never heard that it is an issue today).
5. Some say that women are obligated in the Mitzvah of “Sheves”, but the Aruch HaShulchan rejects this.
6. One of his proofs that women are not obligated in Sheves is the fact that according to halacha, if someone’s husband can’t have children, it is not grounds for her to divorce him (which it would be if she had a chiyuv to have children).
Another interesting thing he says is that women want to get married more than men do. I thought that was interesting because I would have thought the opposite.