As you are forced to sign into the Nook app when you first open it, this is not the issue.
If you did not see this, it means the app did not start correctly.
First, hold the home and power buttons on the iPhone until you see the Apple Logo then release.
Let the iPhone restart then open the Nook app.
It should then ask you to register.
If it does not, close the app, hold your finger on it till it wiggles, press the X and uninstall it.
Then go to the app store, install it again and open it.
It should then as you to register, and when you do you can see your library and books
Let me know please how you go