Oh you poor thing. I'm waiting for mine to come back, had the numbness without much pain in my first pregnancy and the screaming agony, no sleep in my second.
Take paracetemol before you go to bed, buy those sticky on heat packs (for your back) and stick them on your wrists. Then sleep propped up by two pillows, with your arms straight in front of you, your wrists resting on a reusable heat pack each, hands not totally straight, just slightly tilted up. This will get you a few hours with any luck. Heat worked much better for me than cold water. I know why you want to try that, it's the old 'hands dipped in boiling oil' feeling, but heat will ease the pain off a bit better. I have the splints, but did not find them much of a help to be honest.
Stand up and put your arm out straight from the shoulder, palm facing forward. Then bend your wrist back as far as possible to the point where if you were near a wall, you could almost lean on it (so that your hand is at a right angle to your arm). Move your arm from your shoulder in little circles. Do it for a minute or two on each arm. Repeat several times a day on both sides. Bending your hands back will always help a bit, even if you can't tell straight away.
Drink gallons and gallons of water. It really will help, as water retention is part of what is causing the swelling in your carpal tunnel. You may find, like me, that it's also to do with a trapped nerve in your shoulder, and I found a lovely shoulder massage was amazing for that. In fact, do that anyway. It will make you feel better.
My first bout of CT (the not much pain, total loss of feeling bout) took about six months to go after birth. The second bout (agonising pain, hands dipped in boiling oil, couldn't sleep for weeks) went about three days after the birth completely, but was much better almost straight away (basically when I pee'd out all the pregnancy water retention).