Will my family and I get chickenpox?

I (28F) and both my parents and brother never had chickenpox. Grandmother has hid from us that she has a rash on her body. My family took her to the hospital, the doctor made my mum lift my grans shirt and said it's zoster herpes. He said it's not contagious if we had chickenpox, which we haven't. They refused to hospitalize her despite my mum telling them my dad has cancer and can't get sick. Apparently one part of the rash has crusts and other part is just forming. Will we all get chickenpox?