I'm glad you spoke to her :)
It's good that it's a talking appointment.. The doctor or your mum can't make you do anything you're uncomfortable with.
It sounds like you're feeling dismissed from your mum because she's boiling your gender identity down to a phase or part of puberty..
Sadly our parents aren't educated enough about or open minded to the idea of gender and sexuality as a spectrum, the concept of being gender fluid or non binary.. I hope you can feel a little bit of peace in the fact that it sounds like she's has ignorance around the topic and at some point she may be more open to be educated and accepting.
Of course it's natural for your identity to go through huge changes during puberty. In year 7 I learned about gender fluidity and felt that I identified more male.. I cut my hair off and changed my wardrobe, lowered my voice, hated my body for what it was turning into.
Eventually around 15 or 16 I came to a stage where I started identifying more feminine and I feel stable as a female now at 19. But I think going through that part of my life was really hard and full of insecurity, and it was a natural part of figuring out who I am.
Your mum may be right about the fact that what you're feeling is normal, because it is.. However that doesn't invalidate who you are.
Who you feel you are, and what you identify as at this point in time is completely valid and real.. Only you can decide that and feel it in your gut. Naturally it might fluctuate, and sadly you'll have people in your life who will make you question who you are. But point is.. If it's who you are now, then that matters, whether it lasts or not.
Going through the journey of changing your pronouns is a massive step into falling into the identity you fit into.. And it's a journey you might go down forever.. You endlessly learn more about yourself. Your sense of self right now is so fragile (I'm not sure exactly how old you are)..
Your gender identity isn't something you can fake in my eyes. What you identify as now might change, but it is still real and valid.. Just like all the other aspects of our personality. I consider myself straight.. But in the future I might meet another girl who gives me butterflies.. That doesn't mean I wasn't straight before that, and it's up to me what labels I decide to put on myself based on that (if any). It's all a spectrum I suppose.