Note: my experience is limited to the US medical system, so things may be different where you are. However, I definitely agree with getting wrist braces first while waiting for your appointment. Schedule an appointment with a primary care provider who can evaluate you and recommend either medications or refer you to a specialist. Often times carpal tunnel can be managed with over the counter medications, wrist braces, and avoiding the repetitive movements that exacerbate it (usually typing in today’s world). If not, then the specialist of choice is often an orthopedic surgeon that specializes in wrist and hand surgery, though there are also plastic surgeons that specialize in hand surgery as well.

Source: I am a US physician