I get a slight stuffy nose when swimming but can be blowen out easily, and get itchy skin after a week maybe if I don't lotion. Chlorine allergy?

Chlorine irritation. Chlorine is irritating to the parts of our bodies, and can depend on how sensitive our living tissues are to the chemical, and how high the concentration of chlorine is. A true allergy to chlorine refers to reactions of chlorine with our immune systems (think of hay fever, dust allergy, food allergy). One can try allergy meds, but they may not help much if chlorine is directly irritating tissues.