I've had a burning pain in my wrist that won't go away with anti-inflamatories or a carpul brace, what could it be?

Nerve irritation. It could be an irritated or pinched nerve, anywhere from your neck , down to the wrist. You should have your physician look into this.
Many causes . Many things can cause burning wrist pain including tendinitis ligament tears arthritis or even carpal tunnel syndrome. If simple things like medications and bracing do not work an evaluation xray and possibly an MRI or nerve test may be neded.