When people say gender is a social construct, they mean all the things assumed by gender,(Pronouns, wardrobe, body, sexualtiy, etc), as well as the fact that our sense of gender has changed and is still changing throughout different peoples and histories. (one pride identity 2-spirit is actually for people in these cultures that have a gender and or sexuality outside of western social norms.)
Sometimes doing things like changing name, pronouns, wardrobe, and body can make you feel more comfortable with who you are, but that's true even without "man" and "woman" labels. Identity is complicated, and sometimes identifying with a certain social group (again, social construct) makes you feel better about who you are alongside the other things we see as indicators of gender.