Aleve is a catogory C and is not recommended to take during pregnancy. Please consult your doctor for what meds are safe for your condition.
There are certainly a few things you can do...
You can get some wrist splints for you wrists and sleep with them at night. And then of couse try to keep it easy as far as using the hand that's bugging you.
Are you sure it's carpal tunnel and not tendonitis? You can also take an anti inflammatory. There are many anti inflammatories that the doc can suggest and probably some OTC ones.....such as Aleve
If it's really bad and out of control....perhaps consult an neurologist, they may have better ideas.
If you are pregnant, that's really about it, and avoid using your right arm. If you are not pregnant, Ibuprofen and Aleve, and cortisone shots. Worse case scenario having surgery depending on the severity. Good luck!