Ugh, sounds like you ran into an asshole who happened to be trans. Just know assholes exists everywhere, trans, queer, gay, women, men, black, brown, white, Asian, etc.
You were totally in the right to defend your self against them. Assholes, bullies, and narcissists are happy to flip the narrative. This person was harassing you for being a woman, then when you give a comeback, they cry trans phobia back at you. It reminded me of a kid on the play ground who would cuss his mouth out at me, but when I’d say “fuck off” he’d immediately get a teacher to tattle on me for using foul language, of course after he used more foul language than I’d ever heard. The teachers would explain that his behavior did not justify me swearing and I needed to be responsible for my own behavior, not his.
Please let it be known I totally support trans people and consider myself an activist for trans rights. My girlfriend is a trans woman, and I do all I can to argue with TERFS and others who hate trans people.
Yes, your comment was indeed quite insensitive to this (I assume) trans woman, but she clearly was asking for it by ridiculing you for being a menstruating woman. She was actually being cis phobic for saying that to you in the first place, so she’s being quite the hypocrite.
Please know this is not how the vast majority of trans people behave. I know many trans people and all of them are just normal, quiet people living their lives. Assholes exist everywhere and you encounter a bully.
Your comeback was quite clever if you ask me.