Apple id help!!

So, my family and I used to use the same apple id. Since I have moved out and my parents have gotten older, them forgetting the password and me not being in the home cause a lot of trouble. I created my own apple id and logged into the new one on my phone. I made sure to have the old apple id forget my current phone. Now I need to update apps and software but I am unable too, because it keeps on asking for the password from my old apple account. What do I need to do to fix this!!

Thanks!