Neither sex nor gender are “social constructs”: the only social construct here is the idea that sex and gender can be different. It is actually very simple: a person with a penis is a man. You are not “neurologically female” just because you have a mental condition that makes a man want to be a woman. That psychosis should be treated by a psychiatrist, not “validated” by surgery. What you end up with is a mutilated man, not a woman.
Having said that, if the gender assignment surgery has been completed I’ll treat you as a woman; it would be unkind to do otherwise. There is no way a man with male genitals is going to be allowed to use the women’s showers at the local swimming pool, however much he claims to have a “neurologically female” mind. That would be completely unfair to the women, who identify a male as a person with a penis.
Fair warning: unless you can allow for the fact that “trans women” with functional male sexual organs are not women, my piece will make little sense to you. If fact from reading your article I don’t think the world makes much sense to you: the lunatics have taken over the asylum.