The 'evil eye' affects most those who fear it most. While I am not a big user of facebook myself, there are a few things I sometimes want to share with close friends and family. Let's not get all paranoid here about the OP's family casting an 'evil eye' onto the baby. We are not talking about the OP sharing photos of the newborn baby with the whole wide web, but just with her immediate family (mom, dad, siblings, duh). Of course, nothing is 100% guaranteed to be private on the Internet, but Facebook usually does a pretty good job at preventing hacking and private things from becoming public, otherwise they would not have a successful business model. Social media, like any other technological tool, can be a bliss or a curse depending on how you use it.
Anyways, lots of people have babies; I just wouldn't send my photo to someone who is experiencing fertility problems and who may be obviously envious and bitter to see others having babies (and it wouldn't be out of fear of the 'evil eye' that I would avoid doing that but more out of consideration for how that person might feel).