How do I escape a room without a pickaxe?

The simplest solution I can see off-hand is to go to another world:

1. Save and exit the trap world.
2. Go into a different, second world.
3. Make a pickaxe, get a bomb, etc.
4. Save and exit this second world.
5. Return to your trap world.
6. Use your item to make your way out.

I solved my own problem by breaking the torches so it was invalid housing, then saving and exiting. I did end up losing my pick (not that big of a deal).

I hope this solves any future problems.