Pet allergies can be very serious. Some even suffer from allergies so severe they could end up in a hospital just from spending some time in the same home as a pet. Whether this is the case with you, or if you just have some mild discomfort, living in a home where a pet owner previously lived could pose a major problem, especially over a long time of exposure.
It is possible that you didn’t notice it when you toured the house. There is a lot going on at the same time, which can distract you from the itchy eyes and sneezing that starts, but once you have settled in, the reality might settle in as well.
A thorough cleaning of the home can help, but it is important to give attention to any parts of the HVAC system that could harbor a large collection of hair and dander. Replacing filters is important, and if the previous owner left behind some furniture or maybe a vacuum cleaner, these might need to go to the dumpster.