Yeah, that description does sound a lot more like CH. There is a LOT you can do for CH, I've had them for 32 years and managed a 30 year career in law enforcement, a 28 year marriage...( so far

) and raised 2 beautiful daughters to adulthood. Takes some work on your part to educate yourself, and some work to educate your doctor. You have a couple of options, look at clusterbusters.com they look at some "alternate" ways to treat CH, out of mainstream medicine. Their success rates are pretty impressive. Then there is the traditional medical regimen, which I chose...mostly because as a cop the other was not really an option!
A 2 pronged approach is what has worked best for me:
1: A good preventative medication, a med you take daily to reduce the number and intensity of your attacks, that's probably what your doc is attempting with the BP med, is it verapamil by chance? If so, most CH'ers go to a much higher dose then doc's are used to, to get relief. Some go as high as 960 mg a day to get relief. I use lithium when I'm on cycle, at 1200 mg a day it blocks 60-70% of my hits. Topomax also has a loyal following although many refer to it as dopey-max because of it's side effects, it can make you a little loopy.
2: An abortive regimen: the attack has started, now what? Read the oxygen info tab on the left side of the board. I can abort an attack, be completely pain free, in as little as 6-8 minutes using oxygen. It MUST be your first line abortive. DEMAND it from your doc, print out the info from the board and give it to your doc. It's cheap, effective, and no side effects.
Imitrex injectables work as fast as 02 does for me, bit it's expensive, I hate how it makes me feel, and I believe it may extend cycles. That being said I still use it when I get caught away from my oxygen. Imitrex nasal spray works for many, the pills take too long to absorb to work for most.
Energy drinks, rock star etc., any containing the combo of caffeine and taurine, chugged at the first sign of an attack they will abort or reduce an attack for many. If you are taking verapamil, limit the energy drinks, they interact badly with verapamil.
Start the following vitamin regimen: Calcium Citrate with VitaminD, Magnesium and Zinc, washed down with lemonade, up to 4X a day. Alters your arterial PH making you less succeptible to attacks.
None of these are "cures," all are part of a comprehensive attack on the beast to lessen the number and intensity of your attacks, and give you weapons for when the beast breaks thru.
Joe