Hello praxis. I swim regularly as well - sometimes doing the crawl, wearing all the sexy gear (goggles, ear plugs and skull cap), and sometimes I just bob along doing the breaststroke (which is, as you say, is not good for the spine, neck and, in my case, knees).
There has to be a certain amount of chlorine in the water, for obvious reasons, and therefore the face is exposed to chemicals. But I have found that an inexpensive moisturiser or barrier cream (applied before swimming) protects the skin pretty well and when you shower afterwards in fresh water you are left with a delightfully fresh complexion.
I hope this works for you.