Chlorine - are you good for me?

As part of our fitness, eat right plight, I have joined the local swimming pool.  I was once a very strong swimmer, synchronized swimmer and water polo player - now, I am slightly rounded and unable to sink.
So off to pools I went - I have missed it over the years, and have always enjoyed the feeling of my body in the water.  I have been surprised at how many lengths I do and I must say, I do pop out the odd synchro move just for fun (I am a judge for the Bay and I help coach, so I need to remember just how hard it is!!).
But - my skin is suffering.  I get out of the pool and feel very tight all over.  I think my nose is even peeling - it concerns me how much chlorine they stick in the pools.  
So - is there anything good in chlorine???  
Chlorine is typical of a number of nutrients, harmful in some forms and doses but essential for life in others.  We get our dietary needs from common salt, so providing our salt intake is correct, then our chlorine intake should be adequate.
The role of chlorine in our body is:
Assists in the digestion of food
Helps maintain health of our lymph system
Helps maintain correct acidity of our blood
Helps maintain correct action of the liver

The role for my skin..?  NOTHING! Its' fine internally but not externally.  No matter how much I soak my skin or cover it in lotion - the smell is still there lingering...drying me out.  I refuse to use soap or anything with SLS in it, so it's left resting on my skin all day.  But, the swimming - at this stage - is worth it (swimmers bodies are quite lovely) and i will continue to soak my face and lather my body in O'la Tropical Organics on my way to a fitter, tighter me!