Getting your name changed can be a long, bureaucratic process (and there might be more red tape for minors, but I’m not sure.) If you are dead set on changing your name now, then you should be prepared to tell your mom why you want your name changed, how you feel about your current name, why your new name might make you feel better.
Rather than jumping into a heap of paperwork (and potentially hurting your parents feelings if they have any attachment to the name they chose for you), you may want to consider giving your new name a trial run. Start by asking your friends at school to call you by your new name. Start to grow accustomed to hearing it, responding to it, owning it. If you can’t do this step, then you probably aren’t ready to have your name legally changed.
That’s the thing: names are legally-binding things, but nobody is going to stop you from trying on a new name. You could even approach your mom and asking her to call you by this new name. If you grow more accustomed and attached to the new name, and feel like it suits you, then you can consider taking legal action for a more permanent change.
I’ve gone by several different names in different relationships (friends call me one thing, family another, and everybody online knows me by something completely different), but I have never legally changed my name.