Is carpel tunnel an auto-immune disease? does it happen from wrist injury, like a fall, and can it go away?

No, it is not an autoimmune disease. An wrist injury may be a risk factor for carpal tunnel syndrome.

The most common cause of carpal tunnel syndrome is repetitive wrist flexion/extension, from assembly-line work or keyboarding, resulting in a synovitis which compresses the median nerve. Direct wrist trauma can hurt the nerve, but the median nerve can be involved in a general polyneuropathy from an autoimmune disorder. Nocturnal wrist splints can help, and vitamins and NSAID's also useful.