We have 2 dogs and 2 cats in my house.
I am only mildly allergic to them, and it affects my eyes mostly - watering and itchy - if I touch them and then my eyes.
However, I have lived away from home in a house with no animals for over a year, and this still made no difference.
The water which runs into my house is treated with both chlorine and fluoride, as far as I am aware. However, I only drink water which has been filtered. In my bath, I use oats and my emollients.