According to the experts, yes, anxiety can run in families. Nothing you did caused your daughter to have anxiety.
I think the good thing nowdays is we are wiser re mental health disorders and you are in a better position to help you daughter learn ways to deal with her anxiety or seek professional help for her should she need it.
I used to hide my anxiety from my children but these days thay know all my problems and they are my biggest support team.
I wish you peace,