I had this experience when I test drove the P85D. I knew this would happen to me, though. I have a highly sensitive equilibrium/vestibular system, and rapidly changing lateral or longitudinal acceleration will always give me a long-lasting weird headache and/or bring on motion sickness.
After I did a P85D launch I had a mild, foggy headache for the remainder of the day as I expected.
In fact, this was actually one of the reasons I ended up ordering an 85D vice a P85D. I would probably only rarely use the insane mode because I don't want the headaches.
However, this has nothing to do with the Tesla specifically. This is just my body's idiosyncrasies, and I've experiences this on many things including roller coasters, go-karts, aggressive curvy roads in a performance vehicle, and a few others. Oddly, it's only these rapidly changing acceleration patterns that do it. Slow-changing motion like boats or planes doesn't bother me.