what do i do if my family says i am lying when i am telling the truth?

there is a girl at my college getting bullied and i tell my family that she said not to tell anyone so i only told my mom and she blurts it out to my whole family and i get really mad and she said i should tell my brother the details but i told her that i am not supposed to tell anyone but she sid that does not mean family and she thinks i am lying what do i do?