I'm sorry you're struggling so much with terrible headaches. Some causes of severe headaches never show up on any tests or scans, even the newer brain perfusion MRI's. It's discouraging not to be believed or told that "everyone gets headaches" when you know yours are abnormally BAD.
Was your neurologist giving you injections for some form of neuralgia? Were the injections steroids, pain blockers, muscle relaxants, Botox, or nerve blockers?
Some Behcet's research suggests that Behcet's headaches should first be treated the same as migraines with triptans (prescription migraine meds), along with pain relievers, and possibly caffeine to reduce blood vessel inflammation and anti-nausea drugs as needed.
A short course of high dose prednisone helps some patients, but this treatment can't be used frequently. Other options could include neuro drugs such as Lyrica, Neurontin, Depakote etc,, as well as pentoxifylline and anti-depressants. If your migraines flare monthly, continuously active birth control pills might help.
The next step up is often drugs that treat your Behcet's inflammation systemically, such as the biologics Enbrel, Remicade, Humira, and that whole family of TNF inhibitors. More aggressive treatments would include immunosuppressants and chemo drugs.
You can do some online searches for Behcet's headaches and discuss these options with a physician who believes you and is willing to help. I really hope you find something that gives you relief. I suffered from Behcet's atypical migraines along with BD neuro symptoms for years, like you, trying all the above treatments. Eventually my headaches became milder and less frequent.