A toe stuck in an upside-down "V" position is probably a hammertoe.
Some symptoms of a hammertoe include:
Putting on a shoe hurts the top of the bent toe.
Corns form on the top of the toe joint.
The toe joint swells and takes on an angry red color.
It's hard to move the toe joint -- and it hurts when you try.
The ball of the foot under the bent toe hurts.