My hand has a bluish hue, is this a sign of thoracic outlet syndrome?

Not usually.: T.O.S. Usually has neurologic implications(numbness, tingling, decrease in the range of motion of the extremity). Sounds like you are describing something vascular in nature; best to have your doctor check it out and determine which one you are ailing from.

? Raynauds: Blue hands do sound more vascular. If pain is associated, please get this evaluated immediately. If it is intermittent and associated with cold temperatures, stress or tobacco and caffiene use it may be raynauds syndrome. This should be discussed with your primary care provider as it may be secondary to an underlying condition - in severe cases, you can lose fingers.