In my experience, back problems for drummers don't arise so much from posture as from the fact that we schlep all that gear day in and day out. Having said that, good posture can't hurt.
From what you describe, you have decent posture, so I would look more at what else you do with your back. If you carry a lot of weight either in your hands or on your back, are you bending over at the waist, or squatting and lifting with your legs? Are you introducing a lot of lateral movement when you are lifting?
Also look at your sleep habits. I got a lot of relief for my herniated discs when I started using orthopedic pillows for my head and between my legs (ensuring a straighter back line when I sleep on my side). The support of your mattress also makes a big difference, so if you're sleeping on an old hand-me-down mattress it might be time to convince the parental units for something a little more supportive.
Fifteen is quite early to be experiencing back problems, so I strongly suggest analysing your lifting and posture habits across the board, not just at the drumset.
