Explain to her why you want it. That's all you can do because she has supreme rule. But I wouldn't get gauges if I were you. They make humongous holes in your ear lobes that you will probably not want whenever you get older. But It's ultimately your choice.
Say you'll do a lot of chores and if you save up money she can't really tell you that you can't if you buy it on your own. If she still won't let you work slowly at it by asking if you can have them when she is in a REALLY good mood :)
There's nothing really beneficial in getting piercings or gauges. Sure, it helps you "express" yourself but I'm telling you...once you get older, those gauges are NOT gonna look good. No offense. If you're still stuck on getting piercings and stuff, get your own place, be financially stable, and then you'll be able to make your own choices.
I'm a parent, but at the same time I understand why teenagers want to get gauges, piercings, and tattoos. It is what it is. If you love your mom, do her a favor and respect her wishes. Don't do anything until your old enough to do it on your own legally. Your mom is just doing her job, looking out for you and not letting you do something you might regret later
okay, take this step by step. this may take a couple of weeks. 1. mention to your mom that one of "your friends" got gauges. don't make a big thing of it. make joke about it. (wait a week or so) 2.get her opinion on them. and disagree with her in a polite way. (wait a couple of days) 3.mention "your friend" again say that you think they look cool and it's totally safe (wait a week or so) 4.ask her. if you get in a big fight, say that you'll pay for them/ pay her back. if all else fails, yell at the top of your lungs, cry (act childish), and storm off into your room. don't come out to eat (will power), and give your mom the cold shoulder, and let your grades go. do this until she says yes. (will power) this method almost always works.(if i screw up your life, i'm sorry) this what I did to get my hair dyed & what i am currently doing to get snake bites. good luck :)