It just is awfully hard being a teenager, no matter who you are or how permissive your parents are.
Try to think of it this way: your thoughts, wishes, dreams, plans for the future are yours and yours alone.
But some things you just have to put on hold til you are on your own.
I assume you have money to pay for all this, but who pays the doctor bills when it gets infected?
And another view is why do you get to buy something they don't want, even with your own money, while they pay for all sorts of other things you own, eat, use, and so on? Starting with the roof over your head and the groceries.
Does that make sense? (I know it didn't when I was 15...)
Anyway, your parents have 3 kinds of responsibility: legal, financial, and ethical.
Try to give that some thought while you plan your life of independence some day. And maybe save some money for then too. Because you will be in for a huge shock: it's EXPENSIVE, and lots of teens these days end up living at home and hating every minute of it while they endure the same controls and demands.