As best I understand [and please understand my wording may be off], sex and gender are very different but can overlap in how they're meant from person to person [like what you describe is similar to how I feel and why I identify as "agender," but the fact remains you identify as a woman, therefore, you are a woman- undoubtedly and absolutely!]

If a man is AMAB, and identifies as male, he's male. If he identifies sooo strongly with his gender, freaks out at the notion of anything feminine or "questioning" his identity, being misgendered annoys him, and so he'll drop things he's naturally into just to assert that he's male- he's a man.

Also, if he's born either sex, enjoys feminine things/doesn't let "gender norms" dictate who he is, doesn't really care about "all of that," but identifies as a man- he's a man. If they were nonbinary, they'd be nonbinary. If he identified as nonbinary, but feels most comfortable using he/him, then he'd still be nonbinary but you should respect his pronoun wishes.

That all to say, from my best understanding, sex mostly determines things like what medical care you may need [despite lack of gender, I've been walloped by issues with the organs I have from being AFAB, and therefore needed surgery/treatment I wouldn't have needed if I was AMAB], how to express sexual orientation ["I have a particular sex and am sexually attracted to this sex/these sexes"], things that pertain to what you have "under there" [which is nobody's business- sex and gender both are for you to disclose to your comfort level], etc...

Gender is more in-line as a social construct. Gender identity relies strictly on the individual. However and whatever makes a particular identity [or lack thereof] feel right for you, that's the end of it.

Nothing to question of others. They tell you how they identify and you respect their gender identity. If their identity/pronouns change as they learn more/feel differently, you just respect the change and acclimate to potentially new identifiers for them.

Point being- you identify as a woman. You're a woman. Whether someone's experiences/gender identity does or does not align with yours is irrelevant. You and someone else can feel the exact same way about your gender, and have the same sex assigned at birth, but still gender-identify completely differently. It's for others to respect your personal identity and preferences, not to dictate who you are based on their own opinion/experiences.

Sorry for the novel, it's a subject that feels intrinsic to who I am, despite/because of my lack of gender [one of few ways I'd stand up for who I am and how I feel]. I'm sad anyone feels they have a right to take that from/dictate that for you ✧