Are you allergic to all animals or specifically to domestic animals? I would imagine that you actually would find a great deal of places that are off limits to pets and thus you don't have to worry about them, particularly at the wellness spas in town and higher end luxury hotels. Take a look at these: the Smart Hotel Bartolini, Fable and Residence Gloria specifically kept off "pet friendly" as a service they offer, so that is one way you can start making a list of places that would work for you. You could contact them directly to make sure what their policy is.
If you're allergic to other types of animals, such as farm animals, I would just recommend you NOT to consider any farm stay or accommodation in a villa or farmhouse outside of the city as it is likely that there you might come into contact with both pets and other animals.