yes that sounds like carpal tunnel. i had it during my last pregnancy and it was awful. while my fingers were a bit swollen (had my wedding ring cut off halfway through!) my wrists/arms weren't visibly swollen at all.

the good news is that for most people it goes away once you've had your baby. a week after my daughter was born i had no more problems with ct.

i think from memory that icepacks were helpful - rest your wrist as much as possible as well (although that's more easily said than done).