Vaseline

I agree you should avoid Chlorine. Chlorine is toxic. Chlorine is linked to cancer of the esophagus, rectum, breast and larynx, of Hodgkin’s disease and to atherosclerosis and resulting heart attacks. A few dips in the pool won't hurt anyone, but Chlorine is absorbed into the skin and is inhaled. Also, while the Vasoline will help keep the water off your skin, Vaseline and Aquaphor are petroleum based and mineral oil (liquid petroleum) is a by-product of petroleum, which is known to increase the risk of cancer, so I do not advise the using these products in or out of the pool.
http://www.health-report.co.uk/petroleum_petrolatum_health_concerns.htm Yes, you should avoid chlorine. Chlorine is very drying and can make your skin reaction worse.

If you do swim in a pool, you might want to spread petroleum jelly (a product like Vaseline) on the treated area to keep chlorinated water away from your skin.