Am I wrong for having a right to keep things to myself?

Mina
So, today my mom discovered that my Nana(her mother whom she doesn't get along with at ALL) cosigned a vehicle for me aonth ago because I couldn't get it entirely in my name because it was my first car and I'm only 19 so I had no previous history of credit. My mom said she "set me up" so I could lie to her because she asked if the car was in my name and I said yes. Technically it is, I did not lie, however I left the part of my grandmother cosigning out because of their rocky history and I honestly didn't want to hear my mom's mouth because she often tries to make me choose between her and my Nana which isn't fair to me because I have nothing to do with their feud that has been going on since before I was born. Me and my Nana are really close always have been and I will never turn my back on her on turn my back on my mom. I think my mom needs to grow up. However, my mom already knew she would have had to cosign for me when she knows damn well I had no credit. But she just thought she had to "catch me in a lie" and raise all hell. So, today my mother cursed me out and called me all kinds of liars and I "sold my soul to the devil" even taking to Facebook. I told her I was sorry for not mentioning that part but I just didn't feel obligated to bring it up especially with things being the way they are. Am I wrong for leaving that part out to my mom when she is not paying for the car at all (I am) and it's my responsibility?