We tried to do swimming lessons last year at the YMCA but had to drop out halfway through the session because the chlorine was wreaking havoc on Cate's skin.
I put lotion on her before she got in the pool, then immediately put her in the shower upon removal from the pool and lubed her up with Aquaphor. Unfortunately, it still didn't work for us.
We've been told that we should have better luck with a salinated pool or in the ocean, we just can't find one.
I hope it works for you!