Sorry for coming in late, but: headaches that start abruptly (as in "four months ago"), are this disruptive, and keep going on for months should be checked out by a doctor.
You moved three time zones in the middle of the problem, and you are not reporting a big change in frequency/severity. This makes random outside factors less likely. While food can be a cause of headaches, it is actually not that frequent of a cause, and usually a clear link can be found - especially if someone gathers extensive data like you did.
If you really want to avoid medical professionals, try washing out your sinuses with saline (Neti pots often work well) once a day for a few weeks - an indolent sinus infection could be a cause. But if this continues (and especially, if it gets to the point of causing nausea), please try to get to a doctor ASAP.
This has been suggested. Here is a description of severity, and they are a "lifelong issue", it's just the data collection that has been going on for four months.
Also she's apparently getting tested for celiac, but I don't know what that involves.
I've been collecting data about my headaches and diet for almost four months now. I don't see any patterns - annoyingly, I get headaches nearly every day, so there's not much information - but I thought I'd post the data set and see if anyone sees anything. Here it is. Hopefully someone finds this an interesting problem.
It's written in note-to-self format (abbreviations like "strawbs" for "strawberries"; if I mention a complicated dish once then I'll shorten it when I eat the leftovers, as "pasta" for "pasta with artichokes and spinach and pesto"; times given approximately and not in a consistent form and often without specifying if they're a.m. or p.m., though they are in chronological order). Quantities aren't given, although if they're suspected to be relevant I may be able to remember specific instances (for unusual foods) or typical portions (for ordinary foods) - other details might also be recollectable similarly. I also don't notice when headaches go away, so I don't know how long they last except when they last all day or become noticeably worse during their course. My sleep schedule varied considerably over this period, but trends more night owl than early bird (for a while I was outright nocturnal). I moved three time zones west at the end of July, should that matter at all.
I'm not soliciting commentary on my diet except insofar as it can be compellingly related to my headaches.
ETA: Assume that every single day I'm drinking lots of skim milk. (2-6 cups depending on how much I eat and how it's spaced out.) There's a couple of exceptions, mostly when I'm in transit for most of a day or run out of milk, but not many and they don't seem to correlate with headaches.