My pedi said we could have taken DS in the pool over the summer even so I don't think there is anything to worry about. I didn't take him the pool any but did take him to a water park that we have passes to for a couple hours. I was mostly worried about the sun and keeping him in the shade. The chlorine didn't bother his skin at all.
My doc said wait until 2 months and no sunscreen. We start swim lessons next month-- I am just planning to rinse her in the showers and give her a good bath as soon as we get home.
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Re: indoor pool
Both DD's will be in the water by 3 months.
There is no way to protect their skin that I know of.
I think the basic rule of thumb is not before 2 months b/c of chemicals, germs and their inability to regulate body temperature.
After that, the babies are little tougher.