Cat hair can be dangerous if someone is allergic to it or if it gets inside their body by some way. The person can have diarrhea or infection. People can have mild to severe allergic reaction. Sometimes the cat owner doesn't realize that they are having allergic reaction because of their cat and they become sick. So if you suspect that you are having rashes, sneezing or some of allergic reaction then consult a doctor. You should not take allergies lightly and get the right at the right time. The right remedy will be helpful to you as well as to the cat.