In university I had headaches like the Pokémon Psyduck and I didn't know it.
I have heard this. There are certain types of migraine headaches that do not register painfully in the brain. (must be nice) It can result in slurred speech as well as other oddities.
No. If it doesn't ache it doesn't count and if you cannot feel it, it doesn't ache.
Yes, it IS possible to have a headache and not know it. They're migraine headaches which are painless and present themselves a visual disturbance. Years ago, my roommate told her son and myself that she saw the mailbox crossing the street one morning. Of course, we both laughed and then teased her from time to time over the years. She kept saying she wasn't lying but neither of us believed her. It wasn't until years later it happened to me. I was on my way to work one morning and I was waiting for traffic to clear to make a u-turn. As I was sitting there I saw the stationary sign that had reflectors all over it, move quickly from right to left. I asked my primary doctor and he didn't know what it was then I asked my eye doctor and he was the one that told me it was an ocular migraine. Fortunately, it only happened that one time but after I found that out I had to apologize to my roommate for not believing her. But I don't think many people would believe that story. I don't know how well known those kind of headaches are either.