Public pools have much, much higher bather load than a residential pool and many of them are not properly maintained. Indoor pools in particular are a problem because they tend to not use any Cyanuric Acid (CYA) so the active chlorine level is high.
Our recommendation for the Free Chlorine (FC) level relative to the CYA level has the equivalent active chlorine of less than 0.1 ppm FC with no CYA. That's less than 1/10th the amount you find in typical drinking water with 1 ppm FC with no CYA. When you take a bath with chlorinated water (not chloraminated which some water districts have switched to), the chlorine is reacting with your skin about 10 times faster than it would in a pool managed the way we recommend. The FC level is not relevant since you are not drinking the water -- the reaction rates are proportional to the FC/CYA ratio, not to the FC level alone (unless there is no CYA). Drinking/showering/bathing water that is chlorinated does not have CYA in the water to moderate chlorine's strength.
My wife personally experiences this difference between swimming in an indoor commercial pool over the winter where her swimsuits wear out, her hair is frizzier, and her skin flakier compared to using our own outdoor residential pool during the summer where such problems do not occur.