Cluster headaches are the worst pain that exists pretty much... so, your description
of being shot makes me think
of that. Also, they are on one side of the head, and usually around the eye. So... the starting point of your headache sounds like it is in the right place for a cluster headache. Also, them waking you up in the night sounds like cluster headaches too.
These could also be migraines though... if you wouldn't describe the pain as the worst pain imaginable (worse than child birth.