hello from a fellow 16 y/o!
i can relate to your situation, however it seems your mother may be set on saying no. if she truly does not want you to have a snake, then there's not much that can be done except for waiting until your ready to move out. i got my first baby, eclair, at 14, it was difficult to convince my mother into getting her, especially verbally, although what i did to really turn her around was that i went to physically SEE eclair, aswell as hold her, just to really drive the point i was trying to make home.
while im not saying it was a good idea, it was just something i had done to get her!