I somehow read about a study where people were given "brain freeze" by holding ice on the roof of their mouths and that when the freeze subsided so did their headache pain. Okay, I want to start by saying I know a severe migraine won't likely be relieved by this but I DID have some good results with something I tried.
I bought an electric ice cream maker. You freeze the container and then you can make ice cream in 30 minutes. I don't eat sugar so I just put milk in it and added a bit of water so that the machine made an icy frozen milk substance. I tried it with a MILD headache at the very beginning and did get brain freeze and to my surprise that pain did diminish with the brain freeze. It did stop the pain and then the pain was gone.
With a severe migraine (I am honestly not sure to call them migraines and they happen almost always after eating certain foods, msg, etc) it did not make the pain go away but it DID feel icy in my brain and it did feel good in a chilling kind of way. I believe it did alleviate the pain slightly. That time I had eaten yellow cheese and found out it had an additive to make it yellow and that made me so ill. So in that case I had to wait for it to get out of my system but the ice cream did help.
You can also make sorbet in it or you could just put water in it and make a kind of ice with nothing added.
So just wanted to share that.