I have almost the same re-occuring symtom as brently02, execpt mine is on the upper arm in one place. I suffer from asthma and other respiratory problems and was surprised to find this here . . . Where did you see other itchy arm reports?
Have you read the recent comments on "itchy arms" posted this month? Seems like something going on with this!
Chlorine is an irritant rather than an allergenic substance. Shower water contains a variety of chemical substances, including minerals, any of which might cause dry or inflamed skin. Your best bet is to apply a moisturizing cream every day within 3 minutes of drying off after showering. This will seal in the moisture that has just soaked into the skin during the shower, so the skin is less dry and itchy. The best thing to use would be a combination of a moisturizing agent and a sun blocker.