FWIW, Bute did nothing for my horse’s neck symptoms. He also had pretty normal chiro exams albeit he didn’t have the greatest range of motion laterally. He also didn’t have any correlations to working on contact or not, or anything with head position. So, it can be a subtle but significant problem. Even though he did have joint inflammation. For neck and poll, the better temporary analgesic is probably shockwave. Of course after imaging and locating problems there. But I’d expect your issue is more cranial, like at the poll.
I’d also test for EPM—did that with my guy too when he started the spooking because he was just so not himself. It was unlikely he’d be positive and he wasn’t even borderline on the blood test, but at least I got an answer. But considering where you live, you might be more likely to have an iffy test result.