It's almost impossible to add enough chlorine to a swimming pool to make it un*safe* to swim. Uncomfortable for your eyes? Yes. Damaging to your swimwear? Yes. Unsafe? Not as far as I know.
Until just a few years ago, potable water companies (drinking water) could supply you with water that had 10 ppm FC for you to drink and bathe in. In some cases, where they had a problem keeping chlorine in the lines, all the way to the end of the system, they did just that, for customers who lived close to the water plant. Now, they have to *mostly* maintain levels of 4 ppm or lower . . . but if they occasionally exceed that and reach 10 or 20 ppm, they have to tell the EPA about it (not you!) and take steps to 'correct' the problem. So long as they take reasonable steps to correct the high levels fairly quickly, there is no penalty.
I contracted to help supply chemicals and training to large (>100,000 gal) commercial pools for years; I've encountered BABY pools that were accidentally operated at > 50 ppm for a week or more . . . with NO complaints. One heavily used infant pool was operated at 100+ ppm for at least 5 days, before I found it. Again, no reported problems or complaints.
A large country club pool -- ~180,000 -- gallons had a maintenance man who thought he understood pool chemistry better than we did, and dumped (3) 50 gallon drums of the 15% bleach we had supplied into the pool over a 2 day period -- producing a chlorine level of more than 125 ppm. The club had a women's luncheon during this period, and ended up reimbursing members for about $2,500 of ruined fashion swimwear (the LEAST chlorine resistant suits available, in my experience), but had NO complaints of skin problems or other issues.
The club manager and I had a heart to heart talk with the maintenance guy, after I was able to show the manager that our explicit written instructions had been violated. But we kept working there, and kept using relatively high (> 5 ppm) chlorine levels to keep the pool clear, clean, and pleasant to use.

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