What to do when layers of skin are torn from my thumb?

There are hooks on my locker that you can hang things on and I tried hanging my backpack on it but my thumb got caught under it and a chunk of skin came off right next to my nail. It started bleeding real badly so I went to the office and the lady there washed it with warm water and put a bunch of neosporin on it and a band-aid.
It was in the morning and I went to gym afterwards and just left in it a band-aid all day until I got home. Now I washed it with cool water and I’m letting it air out a little. But, I was wondering if I should do anything else besides rinsing it, neosporin, and band-aids? And, if so, how do i do it?