Headaches do not have to be connected to diabetes, but there is good science behind a relationship between migraines and insulin resistance, meaning that you (one) may find migraines improving if you follow a regime that lowers insulin levels, which really means low sugars and starches. If you are taking additional insulin, then the reverse is possible.
But for sure, I cannot say that one thing will lead to the other. I can say that personally I`ve bought and used far less headache medication this year while pushing my insulin levels down. (I appreciate that this may sound confusing if you are being prescribed insulin as a method of control)
I also (before getting my levels down pretty much permanently for the same reason - I was on prescribed insulin for a while) found that I would feel really unwell, very low on energy, and often with a powerful headache, when my levels were changing very fast. I didn't really understand at the time, but these were glucose spikes, and there has been a great deal of press about this kind of thing... everyone is different, but for me I found the rate of change either way to be the most affecting, and have felt so much better when my levels are low and stable.
Water is only useful if the cause of the headache is dehydration... if you are finding that you are drinking a lot, and your levels are high - that's really the primary characteristic of diabetes itself. Can I ask what you mean by "high readings"?
Can I also ask if you have ever had a C-peptide test ? (this is aimed at finding out whether there is any underlying issue with the parts of your pancreas that create insulin naturally)