Could i have an allergic reaction to cold water?

Not really: An "allergic reaction" involves an allergen sticking to an allergic antibody, and water molecules are too small to do that. However, some people have "aquagenic urticaria" or "cold urticaria" which results in hives every time they come in contact with water or cold things like air or water. If it only happens some of the time you contact cold water, it' probably something else. See an allergist.