There can be several reasons for your hand being cold. The main thing is the cold weather we are experiencing here in the US (if you are in the US).....most times one hand being colder than the other is not cause for concern unless you have other symptoms. In that case, the problem could be one of a neurological nature. Other causes would include a circulation problem as if the peripheral vessels are not working well. Raynaud's Syndrome can also cause cold fingers and toes and can be unilateral. I think since this has not resolved on it's own and it has been going on for 'several weeks', I'm sure you are ready to get treatment, so I would recommend that you see your regular Dr first, and then let them refer you out to a Neurologist if they feel like you would be better served with a specialist.
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Anemia could certainly cause cold hands as well...have you had your blood checked lately?