Your daughters can certainly be tested for allergies, if they are showing allergy symptoms. If your daughters are not showing allergy symptoms, testing would not be recommended. The 2 year old can be tested for perennial allergens. It is less likely that she will react to seasonal allergens on skin testing because she has not yet had sufficient exposure to seasonal allergens. Your allergist will decide what specific allergens to test for, depending on the overall symptoms and seasonal variations.
Chlorine can have an irritating effect.
The chemical can cause burning and red eyes, skin irritation and, if inhaled, coughing, sneezing and wheezing. However, in the true sense, this is not an allergic reaction. Allergic reactions involve the immune system. A baby's eyes and skin may be especially sensitive to chlorine, but frequent exposure is unlikely to produce an allergy. Tobacco smoke is an irritant for nearly everybody, more so in people with hay fever and other allergic diseases.