As someone with chronic headaches and eye migraines, I can completely understand that reaction but it's not a surprise that KH3 in particular is causing problems. The other games were running on a different engine at different FPS for the remixes and for 0.2, most of the game was fairly dark and not on the same level of KH3 in terms of visuals.
KH3 has subjectively a rather high base saturation, the contrast is high and it's bright. If you use your usual settings and are a bit sensitive (maybe without knowing since a lot of people are suffering from the Sicca syndrome for example, which are basically dry eyes), you may be experiencing those symptoms.
My suggestion would be to note down your usual settings and play around a little with your TV settings, not the inherent configuration within the game. Turn down the brightness a little, the contrast and the color settings, maybe lean more toward a warm color scheme (that actually makes a huge difference for me if white isn't so glaring and blue anymore) and also reduce the sharpness a little. Make sure the game is not too dark though since that can also create discomfort for the eyes and therefore the head.
It's a bit of a hassle and not easy to find the one you're most comfortable with but different games often require different settings for a good experience.
Another thing you can try is setting your console to 720p and turn off options from the TV to automatically upscale the resolution if you have a fairly modern one that has that. Though that is something that depends on your TV so it may be helpful or not.
I'm not sure the dizziness comes from the fast movement, but you can also try to change the sensitivity of the camera in the configuration.
I'm not sure if you have history of migraines, but long-lasting headaches and dizziness might be a symptom for that or that your eyes are too dry, etc. If changing the setting doesn't work, I'd try going to see a doctor if the problem persists.
Some games can just make us dizzy or cause headaches without an objective reason, too. I've also had games do that, sometimes even from the music alone (Blackwell's Asylum's music made me experience a strange headache and dizziness for three days straight). But in most visual cases, I could reduce the symptoms by adjusting my TV and game settings to a more comfortable one when the TV itself has never caused discomfort before.
I can't and don't want to give you a diagnosis, especially not from afar, but even if it subjectively seems a little worse in terms of intended quality, I'd change the settings to something lower. I also had to do that for KH3 and diverge a lot from my normal TV and game settings because it's simply too bright for my sensitive eyes. Not all games are made for the same base settings.
Make sure your room is well-lit when playing, don't be hesitant to change the settings (both TV and game) if it's not ideal and maybe buy some eyedrops to prevent them becoming too dry as well as sleep and drink/eat enough.
Also look up a few settings which could be counterproductive for games. I read in a few articles that certain settings meant to enhance the picture are actually not that great for making a game run smoothly. You may be subconsciously seeing something of that.
Those are just suggestions from someone with similar problems. It's sometimes not explainable why something suddenly causes problems though if you have no other problems with computers/TVs or other games for the PS4 like I do, I think it may be a case of your base settings being too high/low for KH3 in particular rather than a general problem with your TV/the console or your health. Adjusting them should help in that case.
