Oh my; I'm sorry to hear this; and i certainly know how you feel..I'm sure many of us do.
You're doing the right thing, getting with a neurologist. I do have cluster migraines and cluster feature migraines; I will get up to 9 headaches a day when it's at its worst. Clusters have very defining attributes, they are normally unilateral, tearing of your eye, nasal congestion, agitation, wanting to bang your head on anything.
An icepick is usually very quick, mine have never been associated with swelling or dizziness.
You've had a lot of tests, but I don't see an MRI/MRA/brain angio and I also don't see an cervical MRI; have any of these been done?
I know that your appointment probably seems like it will never get here, but it will and you're going to the right kind of Dr. Do yourself a favor; write a narrative of absolutely everything that you remember. Include any sensation, visual aberrations; funny smells, earaches. If you've fallen in the last year or so, make sure you let them know. It will help to get those things down on paper and it will help the dr. understand as well. Make sure you go with someone; another set of ears is essential.
If you don't think that this Dr. is the right fit for you, I would strongly suggest going to a major university or someplace like John Hopkins, Cleveland or Mayo.
Let us know how you're doing..