It is kind of odd that she asks you how you are in a way that sounds like she thinks you might have a problem but then goes into denial when you tell her about depression. Maybe she expected a different type of problem? I can't offer you any help or words of wisdom but I can relate maybe. I can't talk to any of my family about anything involving depression. They say they care but they just can't talk about mental/emotional problems. A lot of people can't.
I think that if you want to talk to a psychiatric professional then you should do so.
Unless there is something I'm unaware of... it's your decision to make