Creating a new Apple ID

I'm currently under my families Apple ID and just got a new MacBook Pro for Christmas and decided to create my own Apple ID. So I created one when I was setting up my laptop and once I created an account I proceed to log out of the old account on my phone so that way I could login to my new account on my phone as well. When I did this I seemed to have lost random pictures that were in my camera roll. I believe I have to log back into my old Apple ID account on my phone and do an iCloud backup to try to get my pictures back but I'm unsure. I'm just worried if I back my phone up the pictures will go onto my dads phone. If that is the case I'm thinking I'm going to lose all my pictures.