What you are describing sounds like a case of cold urticaria. This condition is an allergy to cold temperatures; any body part exposed to the cold will develop a reaction. This uncommon allergy can run in families, or can be an acquired condition. Acquired cases usually show up when the patient is in the late teens or early twenties.
First of all, try to stay warm. Avoid exposure to cold air, and also to cold water. You do need to take this condition seriously, and you should make an appointment as soon as possible to see a doctor or an allergist to get a professional diagnosis. A doctor may be able to prescribe antihistamines to help reduce the reaction, and may also want to check for underlying conditions. Cold urticaria is sometimes linked to other allergies, most commonly gluten intolerance; if this is true in your case, you may find that avoiding gluten or other allergens in your diet relieves the condition.