I have wrist and elbow pain; is this carpal tunnel syndrome?

No. Carpal tunnel pain is usually an electrical shock or shooting pain in the hand from movement in the wrist. One of the tests is to tap on the wrist to elicit the pain. Elbow pain may be from a tendonitis or bursitis, for example. Wrist pain can be from several causes too including strain. However, one does not get elbow pain with carpal tunnel syndrome.
No. Carpal tunnel syndrome is due to compression of one of the main nerves to your hand. Most people feel numbness in several fingers of the hand (the ring and small fingers), they also complain of fatigue. If this has been a problem for awhile, you may begin to try and protect your hand thereby causing pain in the wrist and the elbow. If this persists you should have it examined.