I am only going to quote some the important bits of your post.
Fortunately, the only thing I experience when gaming other than the feeling of having fun is sleepiness. And that's only after having played for a long while. I looked at the manual of Kingdom Hearts, and it has the same Health Warnings every other game features.
Having not played Skyrim, I wouldn't know; but Kingdom Hearts uses lots of colors and flashing lights. This may be what is causing it.
You should probably consult a doctor, just to rule out any health conditions that you may have. I don't want to sound like a downer, but it may be something serious (signs of epilepsy). If you don't want to see a doctor, the only recommendation I can give is taking a short break every hour or two. Some video game manuals say a fifteen-minute break every hour is best. Not only would it give your eyes time to readjust, but also gives your console time to cool down as well.




But it makes me dizzy and gives me a headache
Oh I am so upset. I've been looking forward to it for ages now. I just finished playing Kingdom Hearts last night and that was giving a bit of dizziness as well. I'm pretty sure there is no way of fixing this! So I am pretty disappointed. It only happens to me when I play certain games, games like Saints Row and Grand Theft Auto give me no problems. It's mostly first person games that give me the most issues. Damn me and my stupid brain!













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