Working as a 16 year old

Hey guys, I'm a 16 year old girl going on to 17 in April and I wanted to ask if I could work under these conditions:
I wanted a job as soon as I turned 16. I want to be able to make my own money and take on the responsibility of a job so as soon as I enter the real world at 18-19 I won't be as afraid and I will have some work experience. I understand that I'm still studying but I know I can handle both, i do great in school and see no problem maintaining my A's and B's. I don't want to depend on my mom for money, since she already has enough bills to pay and it consumes most of the money she does earn. I also want to be able to help her out with bills, even though my pay check won't be enough to make such a significant difference.
My mom receives food stamps and child support, and has told my siblings and I to avoid working as it might affect the amount we receive and ruin the small amount she gets to feed us. My 18 year old brother has a job and she still receives child support because he's going to continue studying, but I don't fully understand why I can't get a job? She says it's because it'll change the amount we get or take it away completely, and I've researched a lot and none of the forums or websites answer my questions fully. 
If I do apply and get a job, will it affect the money she receives? Will it take it away completely? I know this isn't the right place to ask but I'm running out of options, every place I ask or any person I ask doesn't answer me directly.