I wonder if it is the relaxation from alcohol that gives the relief, in which case that would indicate something that is tense or tight is letting go, and the pain eases.
Sounds to me like a soft tissue problem, like sore, tense and knotted muscles. We all have these to some extent, but when we have other problems they can wreak havoc.
You'd be surprised (maybe not) at just how much pain angry muscles can cause. This is what I had-awful headaches for over 20 years. Pain tabs, injections just touched the edges.
My research led me to think I had ON, but my new pain doc found the tight neck muscles.
Remedial massage gave immediate relief, but the problem always came back after 2-3 weeks.
About 6 months ago I found the cure, and have been steadily improving ever since, with not one of those bad headaches since.
I drink 2 teaspoonfuls of magnesium oil, heavily diluted in water, over the day.
Noticed a benefit in a week or 2. Magnesium deficiency is well known as a prime cause of sore muscles.
Just don't expect your doctor to know anything about a non-drug treatment.
You can also get a gel for rubbing directly onto a sore area.
It is magnesium chloride, known as magnesium oil as well.
Highly recommended.