Hi,
Normally
allergy to chlorine is unlikely. It may be sensitivity to chlorine causing stinginess. Otherwise also, if you are allergic to chlorine, it should happen every time. Definitely, some people are sensitive to chlorine depending on the concentration of chlorine in pool water and duration of exposure to this water. Also, salty water can cause this in some cases. Swim suits with mesh may be another reason for this stinging.
Therefore, decreasing the time of exposure to chlorinated water continuously and taking the breaks in between followed by bath in tap water, looking for the chlorine concentration of pool water (If possible), avoiding swim suits with mesh may solve most of the problems.
Just taking a tap water bath / wash of the affected area, is the only required treatment in most of the cases. If the problem still persists, then, you are advised to see your doctor for precise evaluation of cause and treatment accordingly.
Take care. Hope I have answered your question. Let me know if I can assist you further.
Regards,
Dr. Satnarain Bansal, General & Family Physician