Is the splotchiness only on her face? It sounds like the chlorine is drying out her skin. If she has this in other places it may be eczema. My daughter's nephews are black and I've noticed this with their skin. Either way, using an emollient cream without scent should clear it up. It takes a cream made especially for dry skin for it to work. My daughter's sister slathers it on thickly and then spends time rubbing it in.
One brand is Eucerin. There are several generic brands that are very similar and cost much less.