I am 14, I'm a mezzo soprano but I really want to be a soprano (like in opera terms). Will my voice get any higher?
Emily, great question and welcome to the stack. In order to answer your question, there are some truths that you'll need to understand / accept:
1.) 14 is quite, quite young. Like it or not, your voice will very likely not reach full maturity until your early-mid 30's. There is tremendous pressure / expectations from the internet, tv, and music for young people to have incredibly big and powerful voices. This is wrong, for too many reasons to expand upon here. Vocal teachers counsel their students of taking their voices to maturity the proper way, and singing music that is "too big" for a person's voice is the surest sign of immaturity. People who sing too big too soon do not have long careers - they might sound terrific for 20-30 years, which to you might sound like a long time, but a properly maintained voice still sounds incredible after 50 years of singing professionally.
2.) I mention all that for context of my second point: choose your music carefully. You should know that when composers write vocal music, they write for the person (or they should anyway, if they're a good composer and decent human). Over time, we start to see trends in ranges, and from those trends, develop rough ideas about voice-types. Not all ranges are the same. Not all people are the same. I say this because you might really want to be a soprano, but that just might not be your voice-type. If it's not, it is wrong, and can even be damaging to your voice. However...
3.) Know that just because you or your music teacher classify you as a mezzo now doesn't mean you're locked-in for life. Perhaps your music teacher just has too many sopranos and needs lower-voices to fill out the sound. Maybe you just have a very intuitive lower-range. Doesn't matter. Many vocal students are re-classified during their collegiate / conservatory training as their voices develop and their voices mature. Classification, like your vocal range, is fluid (i.e. not set in stone).
4.) Over time, as your voice matures, you can undertake exercises and techniques to broaden your range and strengthen your sound. This should be done with a vocal teacher for guidance.
In sum, don't be in a rush. If you take care of your voice, your voice will take care of you. Always choose music that fits your voice; you shouldn't try and squeeze your voice into a piece just to have the satisfaction of squeaking out a couple of high notes. It looks immature, no one wants to hear it, it doesn't feel good for your voice, and prolonged use could even lead to vocal damage.