Can a case of severe allergic skin reaction be related to water intoxication?

Probably not: Allergic reaction r usually mediated by an antibody called ige in the body. Ige has to bind usually large molecules, such as proteins to cause an allergic reaction. Water molecule is very small. It will not be recognized by human ige. So no one will be truly "allergic" to water. In the rare cases of aquatic urticaria, contact of skin to water can trigger hives, but not a true allergic process.

Water non-allergic: Allergic reactions occur because allergic antibodies (ige) attached to the cell membrane of immune cells called mast cells bind to a foreign protein they recognize, activating the mast cell which then releases histamine and the histamine then causes the allergic symptoms. Allergic antibodies are only formed to large molecules, usually proteins, which are many thousand times larger than water.