It's not the same as what I would describe as brain fog, brain fog is almost literally that, it's trying to think inside an increasingly small space, as the space gets smaller and capabilities become outside of the area that can be accessed ( think big room, single dimming light, you can only access things you can see, as the light dims, less capabilities can be used, less fully, until even mental movement becomes impossible). Pushing against this is possible, it's fog, upto a point it's soft, but pointless, as it simply results in the fog hardening (increasing in viscosity), discomfort and the light dimming further. It's unpleasant, it's limiting, if ignored it can be very unpleasant, and crippling - but it's not actually painful per say.
That's one, far from complete, description of what I experience of brain fog.
The "horrible sensation" is different. It's a pinching, crushing, ripping, tearing, both feeling very specific but vague, sensation. It is analogous to pain. One aspect of it, "I" am a vortex, the more I try and think the faster and narrower the vortex becomes, the rest of "me" is outside the vortex, my learned abilities/knowledge. I can, until it gets too fast, reach outside the vortex to use capabilities that aren't inside it, but as you would expect, reversing the analogy, shoving a hand into a hurricane to grab something inside it, control.accuracy is really quite tricky, and the process hurts. Trying to access them, the possibility/difficulty is dependant on the vortexes speed and how far outside it they are, how small the vortex is relative to that which is "me". The attempt hurts, speeds up the vortex, making the attempt more difficult, rapidly making it impossible, ripping at "me".
The difference between brain fog and it may be analogous to the difference between walking through a field of sheets hung up to dry (can't see far, some resistance, trying to get anything done is, problematic), and repeatedly running nose first into a wall as fast as you can. *edited to add - or maybe repeatedly standing on rakes ala sideshow bob
The only solution is to stop, everything, until things slow down again.
Bonkers sounding I know, and not literal obviously, it's just a way of trying to explain a small part of it, a not very good or accurate way - but it was the best I could come up with a few years ago last time I tried.
"horrible sensation" covers some of it, and is much more succinct, and doesn;t make the poster sound nuts, that description, plus other agreements, points raised in other post, matches what I experience, just using different concepts/words.