I have been scratched and bled by a domestic cat for three months. The domestic cat is normal now. Will you be infected with rabies?

Usually not. According to the first report of WHO rabies expert consultation published by the World Health Organization in 2005, if the injured person is a controllable cat, the cat can stay healthy for at least 10 days after the injury, and the vaccination can be stopped. You say that the cat stays healthy for three months, then you generally won't be infected with rabies.