I have a chronic daily headache, are there any surgical options for me?

Possibly . There are two chronic headaches that currently have reliable surgical options: 1. Trigeminal neuralgia (sharp, stabbing facial pain that can be triggered by eating/touch) and 2. Occipital neuralgia (neck and occipital pain from an injured occipital nerve). Common headaches, migraines, stress headaches, and cluster headaches are all headache types without surgical options.
Yes. Surgery not the usual treatment, and cannot speak about your headaches in particular. Never blocks including the greater occipital nerve and stimulators implanted into a variety of nerves in the face and neck, are often used.
Probably not. In general there is no surgery for common headaches.