I got hit by a whirlwind in the mines in the spiky area and stuck near the wall, able to turn in place but unable to move. Is there a way to unstick myself without restarting the level?

Hm... that sounds like a bug of sorts. I tried reproducing that event but was unable to do so...

Let's hope someone else has a more in-depth answer to give you, though I would think that, unfortunately, you will have to restart the level, indeed... :\