Can you be allergic to chlorine?

Yes: You can be sensitive and rarely allergic to chlorine.

No: Being "allergic" means that your immune system is making an allergic antibody against some type of protein, for the most part. Chlorine is an atom or a small molecule - too small to be recognized as an allergen. It is, however, a potent irritant, and will be much more irritating to people who already have inflammation in their nose, sinuses or lungs from allergies.