No, gender is a social construct and the doctor is assigning a gender to you when you are born based on what he sees as your genital configuration. This is then used to determine nearly everything about you through the social framework of gender.
What colors you’re allowed to like, what games you can play, what names you can have, what words are acceptable to refer to you with, who you’re allowed to be friends with, what foods your supposed to like, what clothes you’re allowed to wear, how people should speak to you, how people should praise you, how people should scold you, whether or not misogyny should be applied to you, and so on and so forth.
Those things are determined based on the gender you are assigned at birth. Those things are enforced across all society at all social levels and in all settings. Parents are the first people to enforce gender onto their children, intentionally or not. Then every single other adult and child they meet or interact with throughout their childhood will continue to enforce gender upon them until they themselves become adults and repeat the cycle with their own kids. Media perpetuates gender, government laws enforce gender, education systems are filled with people who systematically enforce gender upon children.
Thats what we mean when we say gender is a social construct. And you’re assigned one at birth.