I'm curious about why you disregarded the diagnosis of tension headache.
I had these for many years, but you don't need to feel tense to experience them.

The tension refers to muscle status. So tense muscles pull on the vertebra and joints, putting them under stress and strain. This can then lead to nerve impingement and sharp pains.

My tension headaches were caused by very tight neck and back muscles that were pulling down on my neck. Awful, awful headaches.

My (eventual) diagnosis was from a pain doctor. He suggested remedial massage, then a daily exercise routine. That is what I did.

The massages gave instant relief, but needed to be done very frequently at first, as I was a mess.

Later on I found that a magnesium supplement fixed my muscle problems, and now I don't need massages at all.

You may be surprised at how much pain tight muscles can cause. Well worth looking into.

From my experience over many years, general practice doctors are able to offer very little in this area.