So um how do I get my accounts?

As far as I know, its basically impossible to get an account without the code.
Is it actually updating at all? Or is it just forever stuck at the update screen at 0%?

Nope. You need the code

Short of rooting your phone and using Titanium Backup there's no way to do it.

Always ALWAYS make a code and write it down. Even if you don't need it right then. Turn this into a learning experience.