I re-entered the test of courage after creating the sword and after i kill the dragon the door to the north of the room does not open and there is no way to open it. The dragon is supposed to open before he leaves but that isn't happening. Any ideas?

I'm not sure how or why it wouldn't open. It's been a while.
But if there's no way to open it, you can enable the 'Hack Mover' to drag the door out of the way.

If you're using the vanilla game, you'll need to enable the cheats to do so.
There are a number of topics about how to do this, like this one:
https://www.gog.com/forum/ultima_series/ultima_7_original_cheats
When in-game: Press F2, H, and escape.

If you're using Exult, just press Alt+H, and drag the door.

Be sure to disable the Hack Mover again, or you'll accidentally drag stuff to places where they shouldn't be dragged.