The chemical that you smell in the atmosphere and stings your eyes in the water is not chlorine but a chlorine reaction product called trichloramine.
Trichloramine is toxic, it will strip the mucous lining from the lungs of children and predispose them to infection. Trichloramine also elicits a sensitised reaction which is reinforced by subsequent visits to a pool. The lungs remain sensitised until the mucous lining is restored, but for that window, exposure to other chemicals, dust, pollen or mites etc, etc etc can manifest itself in an allergic reaction that may develop into asthma 10 or 15 years after exposure. We know this for a fact, the problem is that it will be very difficult to quantify, and because it can not be quantified nothing will be done to fix the problem.
Unlike the rest of Europe, there are no statutory standards in the UK for pool water treatment system design, and there is no certification of any products or chemicals used to treat the water. By way of example, the total combined chlorine levels in Germany must be below 0.2 mg/l; in the UK concentrations over 1.0mg/l are common.
Next time you visit a pool, ask for the water analysis records, if the combined chlorine level is below 0.2 mg/l and the Pool Performance Factor is less than 4, then the pool is safe to use.