What helped me a lot was inserting my fingers and thumb of one hand into a medium sized rubber band and pressing outward against the band. As my hands got stronger, I would try rubber bands with more resistance.
I'm not sure why it worked, but it did. Maybe it increased my circulation (I held a lot of water when I was pregnant). If you let your hand go limp and squeeze your arm just above your wrist your fingers of the limp hand will curl slightly. If you feel the top of your arm just above your wrist as you extend your fingers, you'll feel some muscles working there, so pressing outward works out the muscles of the back of your hand and the top of your arm and that may help to keep that narrow carpel tunnel channel open a bit more so the nerves that run through it don't get as pinched. I work with computers, too and I still work my hands out this way from time to time and they feel great. To get the excess fluid out of your hands first thing in the morning, sit up, and put your hands in the air over your head for a few minutes. Drink plenty of water during your day. It helps your kidneys flush out your system and can reduce the excess water your body is holding. You are not only eating for two. In a sense, you are also peeing for two, so your kidneys are working harder than usual.