Sounds exactly like carpal tunnel syndrome. I would strongly urge you to ask your primary care physician for a referral to a neurologist to get tested.
I had the same as you - shooting pain, tingling, numbness that surfaced during pregnancy, and was surprised to get the diagnosis b/c I thought it was only people who type on computers all day that get it ;-) Be sure you are not dehydrated either, as that makes it alot worse. The pain will likely get worse as you get further along (due to extra weight and fluid retention) but there are alot of lifestyle changes and hand exercises that you can do to manage the pain. A neurologist will definitely be able to help you. You can't really avoid the braces at night, atleast I wasn't able to. But I got used to it and hopefully you will too. Good luck and I hope you get a diagnosis soon.