Would this be because your head is closer to your feet, or (and correct me if I'm picturing this wrong) because you're putting your head upside down?
https://my.clevelandclinic.org/health/body/21778-nose
There is a number of sinus decongesting massage moves that work well. These use pressure and blood flow to force the liquid out of your sinuses and then uses gravity to take it away. I use these to help relieve sinus pressure.
https://health.clevelandclinic.org/sinus-massage/
But, to answer the original question, this is only related tangentially. Laying down, picking up your feet, and breathing generates a signal in your Vagus Nerve complex that essentially overrides the fainting signal. It’s still there, but you’ve added a new stronger signal to dominate the nerve and the fainting signal starts to fade. Simple meditative breathing does the same, but usually not fast or strong enough to stop you from syncope.
https://health.clevelandclinic.org/what-does-the-vagus-nerve...
Oh, no; the motion I'm referring to doesn't involve moving my head at all. I meant that I raise my right knee while balancing on my left leg, to scrub my right calf by bringing it into reach. (Is this not how most people clean their legs in the shower?) Doing this — and holding the pose for at least a few seconds — almost always unplugs my right sinus. (And only the right sinus. Have to raise my left leg to unplug my left sinus!)