I have shooting pains and sometimes numbness in my thumb which leads to my wrist and goes down my arm sometimes. Is this a sign of carpal tunnel?

Carpal tunnel. numbness in the hand especially in the thumb index and middle fingers can be a sign of carpal tunnel syndrome. It can also cause pain in the wrist shooting up the forearm. A nerve conduction test and EMG is sometimes needed to make the diagnosis.
Pain numb thumb. Yes these are symptoms consistant with carpal tunnel syndrome. Often caused by overuse or irritation of hand and wrist e.g. Computer typing or mouse causing repetitive tissue injury in the hand and wrist. See your doctor for help. Meanwhile cut down on excessive movement of hand and wear wrist brace.