I used to get terrible pressure change headaches - they're fairly common around where I live. I've known people who have had to leave the city because them, and I almost did so myself as I didn't want to be at the mercy of the frequent pressure changes. These headaches can be cripplingly painful, making it hard to function without painkillers, which I'd personally prefer to avoid wherever possible. And nature's best painkiller isn't always practical when you are required to perform certain duties.
Luckily, I cured my headaches by using a neti pot, which has been mentioned (I lol'd at your little image there, Cheers!). Here's a helpful site with some instructions and tips:
Jala NetiI don't bother with the saline packets - I just use a little pinch of sea salt added to pre-boiled water from the kettle (1/4 tsp of sea salt to 8oz of water is about right.) I let it sit until the water's luke warmish, body temperature-ish, and then go for it. It does take some getting used to, but with time it gets easier. I mentioned on the old boards that when I first started using mine I had a moment of panic, like I was going to drown! I reminded myself that I was perfectly able to still breathe through my mouth, lol.
Anyway, I used it consistently for a few weeks when I realised that I hadn't had a headache that entire time. But then when I stopped for a few weeks (got super busy, plus I have issues with routine and discipline -

) the headaches came back. So I started using the neti again and my symptoms lessened almost right away. I rarely get headaches at all anymore and whenever I feel one coming on I use my neti and it's gone!
I now recommend the neti pot to anyone who suffers from these migraines. A few things to remember: keep your pot clean to avoid bacterial growth, and don't use tap water straight out of the tap as it will burn. If you start to notice water in your ears or dripping out of your nose throughout the day, then you aren't getting the angle of the head right and you may need to tilt a little more so the water can flow out more completely. Let me know if you have any questions.

Oh! One more thing - I am a lifelong allergy sufferer - mega-allergies - and even my allergies (which I now fairly successfully treat homeopathically) seem to have lessened since I started "neti-potting". It's worth a shot!