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You are suffering from a condition called 'cold urticaria'. Some people are allergic to cold, whether cold weather or cold water. The cause is unknown but is believed to be due to the skin being more sensitive than other people and releasing more of a substance called histamine.
The symproms are the ones that you describe - itchy, red skin on exposure to cold, swelling and hives on scratching..
Treatment is by antihistaminics like benadryl. You will need to be examined by a doctor and if the condition is severe, need prescription medicines.
Please see here for more on cold urticaria:
I hope this helps.
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