Have you actually had it diagnosed properly?
Carpal tunnel syndrome (CTS) affects the thumb, 2nd, 3rd and thumb side of the 4th finger and usually doesn't cause symptoms past the elbow.
Neck problems cause symptoms from the neck down to the hand.
There are rarer problems such as problems with the brachial plexus in the shoulder/armpit area or even the roof of the lung.
The treatments are different. CTS can be treated with a wrist splint to be used night-time for sure and sometimes in the day; also relatively easy steroid injection.
Then there's ulnar nerve pinching, usually at the elbow. it affects the 5th finger and the nearby half of the 4th finger. But you say your syndrome affects the thumb(s).
All 3 can affect grip.
You can't treat a problem till it has been correctly diagnosed.
Unimog U500 w/Unicat