I just checked out some of the recent conversations about Chlorine on Twitter. Lots of people notice that they still smell like chlorine despite showering. Here are a few examples:
Notably, showering (even with swimmers shampoos) does NOT wash the chlorine out of your hair and skin. Accordingly, swimmers notice that they smell like chlorine. To get rid of the chlorine (and the smell), a swimmer can rinse off with Vitamin C, for example by using SwimSpray.