Silver nitrate on baby’s belly button

Our pediatrician said our one week olds belly button stump wasn’t allowing proper air flow to get in so he moved it around and applied silver nitrate. That night it fell off *yay* but now a few days later her belly button is now black and has what appears to be dried old blood / maybe a bit of stump remnants. I was told to apply rubbing alcohol to help get rid of it but I’m scared as the hospital said alcohol was no longer used for belly buttons. I know our pediatrician obviously knows what he’s talking about but has anyone else had the silver nitrate done and had a similar experience? this is what her belly button currently looks like