Thanks for the reply...
Apparently after speaking with my grandmother she claims that somewhere along the lines the name was spelled Barzola instead of Balzola. She doesn't know which relatives but says that on some docs it was spelled one way and others another. Soon enough they eventually just started spelling it Balzola as I do now. She could not however tell me who, when, or why this change was made. Unfortunately, I've looked up the alternative but it's been almost impossible to decipher if they're part of my family or not. I'm still trying to decipher whether those with my last name are even part of my family.
Most of my grandfather's family have passed so it's been a daunting task and my grandmother was the one who's been giving me much of this information. I don't really speak with my other relatives so I don't really know where else to turn.