I oscillate between very hot water on my head to a cold cap. I have some neoprene helmet like things I keep in the freezer.
However, one thing that you may be interested in is Sumatriptan. I don’t know your situation, but I get sinus pressure during migraines, along with color changes and field of view diminishing before onset. Migraines are a very strange beast poorly understood by science and not consistent from person to person. But a shot of sumatriptan is a miracle for those it works for if you get it in time. Like, within minutes, I feel quite strange and the symptoms slow and the headache either doesn’t come or is much less severe.
I just want to clarify that sinus headaches and migraines are completely different. I’m just saying sometimes sinus issues come with migraines. This applies only to those cases. And I suspect it can be difficult to tell which is which in some cases.