There's a new sign up at the one pool I go to, that tells how to avoid that chlorine smell. According to it, chlorine attaches to fragments of both hair/skin and soap, so they recommend:

1. washing well with soap before swimming, and rinsing off well
2. showering without soap (and shampoo I presume) afterwards.

I can't vouch for the chemistry, and I don't know if it helps against green hair, but I do know that I smell a lot less of chlorine once I started following these tips!