Not sure on how you should make money. I would try thrift shops, because a lot of the time you can find items that are new. Also, Old Navy has some cute clothes. The clearance racks will be your best friend anywhere. But, at Old Navy they have shirts and jeans down to like $5-$10 !!
Try upcycling :-) its a fun way to create new unique clothes. You could also go to marshalls and stuff. Also if you have an iPhone search for feature points and use this code: XSMQSR you basically download apps, earn points, and use them for rewards like money on Amazon or Paypal
You can try things like babysitting, yard work, dog walking, cleaning, etc. for neighbors, friends and family. There isn't too much you can do at your age, but just try to show your interest in making your own money to your mom and maybe she'll appreciate it. If all of that fails, then ask for money for birthdays and holidays and save it so you can get some new clothes. Forever 21 has some really cute clothes for pretty good prices especially in the clearance section. Target usually has nice clothes, too. If you have a Marshalls or TJ Maxx in your neighborhood, i would defiantly check out their clothes because they are very cheap as well. I'll put Forever 21's link at the bottom, and they are in most malls as well. Hope I helped and good luck getting some new clothes!