Try to sleep. Insomnia=not sleeping. It doesn't mean getting shit done in spite of no sleep.
There's no such thing as productive insomnia. That's just mania, and anyone who tells you they do shit when they can't sleep is bipolar on the quiet tip.
Note: If you can't sleep, you're actually not supposed to lie in bed for more than 15 minutes because then you start to associate your bed with the inability to sleep (a la behavioral conditioning).