You would have symptoms like these (source CDC):
During or immediately after exposure to dangerous concentrations of chlorine, the following signs and symptoms may develop:
Burning pain, redness, and blisters on the skin if exposed to gas. Skin injuries similar to frostbite can occur if it is exposed to liquid chlorine
Burning sensation in the nose, throat, and eyes
Difficulty breathing or shortness of breath. Thesemay appear immediately if high concentrations of chlorine gas are inhaled, or they may be delayed if low concentrations of chlorine gas are inhaled.
Fluid in the lungs (pulmonary edema) that may be delayed for a few hours
Nausea and vomiting
Showing these signs or symptoms does not necessarily mean that a person has been exposed to chlorine.