Immeadiate effect? Even in migraine preventative treatment the use of that is cumulative [have to take them for a while for the effect to build up]
In other words by the time its built up enough to be effective if your episodic you may well have left this cluster cycle anyhow.
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Keep fighting your corner, your the one who is living with these symptoms. Had a thought, if you have a camera could your partner take a photo of your eye when it droops and waters? 'Horners' does not alway oblige in the 5 minute UK GP appointment slots and it is one of the big pointers that you do need to see a neurologist.
Have to admit even I have gone to A&E when the pain has eaten me alive - with my brood in tow. The pain can be so awful sleep is not a choice at the time; try and get some rest in between hits if you can.
This time I did not begin to catch up on weeks of lost sleep until the heads ceased and I could sleep.
My kids have survived on cold baked beans out of a tin with rich tea biscuits to dunk in the sauce whilst watching mindless amounts of kids TV when they were younger and I was bad. It was not ideal but at least they had food.
IF you have a pattern to the pain I suggest trying to make food ready to microwave or similar later, the freezer is your friend.
Ready prepped fruit, bread rolls, cubes of cheese or whatever protein they like in a sandwich box in the fridge make a good instant lunch that even a three year old can get for themselves if you know lunch ain't going to be great.
I even planned my days around when I knew the pain would surface; mine likes to wake me up at 4am and smack me 4 to six times a day for fun when its back. I know I am a choclate fireguard when it hurts and will be delicate and achy in between but I can target one or two goals to try and complete each day.
Choose your essential battle for the day be it the washing up and basic food prep for later or keeping that promise to take them to playgroup for a bit and collapse once you get home having used crisps, bread and bribery for half hours rest. If you manage something great and if you do a little more fantastic.
Even three year olds will pick up something is not right with mum so try and explain that sometimes mummy's head hurts like someone has hit it with a hammer and it is NOT your kids fault but they can do X, Y and Z whilst is does hurt as that would help you.
I also taught mine how to call 999 'just in case' after a memorable falling down the stairs and having to be dragged off to A&E with concussion after one really bad headache just started.
I also bought a phone with programmable speed dial so my kids could call 'Dad', 'Granny' and 'Grandpa' without trying to remember the long phone number. I know I can be pretty ill and decided my kids knowing who to call for back up would be less scary than worrying over what to do when I am bad. [Hope that makes sense]
Welcome to the world of creative parenting CH style.

and trying to explain to GPs who think its all stress because your trying to care for young kids.
Ha perhaps when i have time I may try and write something on parenting with head pain!