Chlorine smell is due to the chlorine and chloramines layered on the skin after using the pool. So removing the chlorine and chloramines contents are the solution to remove this smell. As soon as you exit from the pool, stand in the hot shower with the max temperature you can for at least 2-3 mins. Then lather with your regular natural soap for some time, allow to dry and then wash thoroughly with hot shower. This removes the maximum chlorine on your skin and then you can try out the following methods.
1. Mild acid solution: This will not harm the skin. Either you can use citric acid or acetic acid. (a) Squeeze and dilute the lemon (1:4 with water) or orange (1:2 with water) and apply on your body for some time and leave it to dry. This acid will eat away the chlorine. (b) Use white vinegar for acetic acid and dilute with water, say 1:5, and apply on your body and wait for some 2-3 mins. Then take a hot shower.
2. Vitamin C removes chlorine. Ascorbic acid in the vitamin C gets away the chlorine smell. You can buy vitamin C crystals from shops. Dilute with water, apply on your body, wait for some time, say 2-3, then rinse with hot water. There are vitamin C creams available on markets, same procedure after applying. These two products are not so costly.
3. Minimize chlorine exposure: (a) Apply oil before entering the pool. Olive oil or coconut oil can help better. This forms a protective layer. Rinse with hot water on exit from the pool. (b) Beeswax or butter are also the other options for this method.
4. Club soda also helps. Rinse the body with club soda and then take a hot shower.
Technically speaking, chlorine oxidizes on skin. It chemically reacts with the surface of the skin and forms a layer of chloramines with hydrogen. Mono chloramines are more stable and do not dissipate as rapidly as free chlorine. Any antioxidant will help to release chlorine's bond to the skin. Then the chlorine easily washes away. Applying any fruits with more antioxidant will help to remove the skin. Then take a hot shower.