How do I convince my mom that I'm Serious?

I came out as transgener to my mom about a year ago, but at that time, she said something along the lines of, "I don't think you're old enough to know that." That kind of got me upset, but I just figured she didn't know. Other than that she seemed supportive and said we could do research and maybe talk to my doctor about it. After a couple weeks, though, she stopped talking about it and I didn't know how to bring it up so I never said anything.

Somewhere in between then and now, I had to dress fancy for a school band concert, so my mom was giving me some pretty feminine clothes. I said something like, "I already told you I don't want to have to dress in those types of clothes anymore," and she didn't understand so I got pretty upset. Later, I heard her telling my dad how "I completely overreacted over clothes," and I realized she thought I was just a tomboy who didn't like feminine clothes and that I "got over that phase."

I know she didn't realize that she was being rude, but it still hurts. What can I do to let her know I still want to be a boy? Do I have to come out again?