I hurt my wrist practicing the piano on Saturday. What should I do for it?

Yes, yes, an injury from piano… Bizarre, I know ;)

I twisted and stretched wrong because I was learning a knew song and didn’t know where exactly my hand went. It instantly hurt, although it wasn’t bad enough that I had to stop practicing right away. I thought I had just stretched a muscle a bit farther than I usually do, and it’d be sore for a few minutes and then go back to normal. So much for that. I realized I had actually injured myself on Sunday morning, when it started really screaming at me. I used a heating pad on and off all day Sunday, because it made it feel a lot better. Monday was fine, and I thought I was back to normal, but when I went to my piano lesson on Tuesday, it flared up again and my mom bought a brace like this for me. I’ve been wearing it on and off for the last two days, and I’m starting to realize my wrist/hand isn’t getting better, although the brace helps.
So my questions are:
-How can I know for sure whether or not it’s carpal tunnel? It seems to fit everything I’ve read on the internet, although a friend told me it absolutely cannot be carpal tunnel because I’m only 16. It seems to me that anyone who does repetitive movement (like typing or playing the piano) without being careful to always move properly can have this happen. So can I definitively say “that’s not it”?
-What else is there besides carpal tunnel? I really don’t know much about wrist injuries. Articles to read would be helpful.
-Is there anything left that I can try on my own to help it recover? Or have I tried all my options and should go to the doctor?
-Should I be wearing the brace all the time? Only when it hurts? -Should I be pushing it and trying to do everything I can without hurting, or should I completely let it rest?