Private disability you can get pretty much immediately, they are required to follow a doctor's instructions that you are disabled. If they balk too much, threaten to contact the state insurance board and it will miraculously be covered. You do have to keep looking for a treatment that works, but you'll probably do that anyway.

SS will probably deny you until you appeal to a judge. Legally they SHOULD cover you immediately, it IS insurance so you have a right to collect it, but they make you jump through so many loopholes you might find it easier to hire an attorney. They usually have some sort of plan in place that takes a percentage of the money you are owed in back pay, but once you get it future payments are all yours.  It takes more than a year to get unless you have other serious complications. Make sure you include EVERY diagnosis in your application, including things you may not think of but probably have like depression. In between hits you may not be depressed but if you get such severe hits that you have suicidal thoughts you would be classified as severely depressed (If you have suicidal thoughts in between headaches you may want to check yourself into a hospital).

I am on SS disability.  Was approved the first try.  I had a long history of jobs gained and lost due to hospital visits/admits and just plain bad times with my chronic CH.  I gave a ton of documentation from doctors, hospitals, treatments, jobs, and information about clusters.  I believe it took 3-6 months for the approval letter.

I was chronic and got 8 ch a day every day lasting 1 1/2 hrs each.  That is kip 10's 16 hrs a day.  I could not function at my job or as a parent.  Life sucked.  I was depressed and suicidal.  I also suffered from migraines.  I got 8 of those a month as well.  I had tried everything on the market and nothing worked for me to prevent the ch or migraines.  I was in the ER 8+ times a month every month and hospitalized many times for ha.  I had letters from employers and coworkers and drs.  I applied for SSDI for ch, migraines and depression.  In 6 months I was approved for SSDI NOT because of the ch or migraines but because of the depression it caused.  I had to meet with one of their shrinks by the way and was only temporarily approved.  They thought the depression would get better after 2 years.  It didn't but I found a way to prevent my ch and migraines with opiates prescribed by my dr.  I have been pain free for 8 years.  However I still suffer from depression and schizophrenia and have a bad back.  So I stay on SSDI.  It has been 8 years now.  Good luck applying.