I think the allergy such as skin irritation is related to microorganisms of water. hence. it can be a good idea to analyze organic matter and type of microorganisms of the water. it's good if you can determine anthropogenic inputs to understand the probable pollutants.
It is probably related to micro-organisms as mentioned by Mohammad. You can read Sinton et al., 1998 and Gourmelon et al., 2010 to get more informations about faecal contamination management.
Perhaps it would be good to check, whether and how the drinking water is desinfected. High levels of Cl may also cause irritations. It would be also good to check ph-values, as extrodinary pH can also cause skin irritation.
Check first if there are allergens or akaraia in mattresses, blankets, air conditioners etc.
Heavy metals causes irritations after exposure to high concentrations for a long time. Microbes (especially anthopogenics) would cause intestinal or stomach upsets in high concentrations. High levels of Cl may cause irrigations but with high Cl no microbes are present. Finally, pH in most natural waters are neutral or slightly basic.
depending upon what is in the contaminated water. Different people have different reaction to certain chemicals. Some people are more sensitive to others, and more sensitive to one kind of chemicals than others. Need to be specific.