I have GOTTA admit "hangover"....you hit that nail right on the head.
I've been suffering now for over a year and a half with migraines and vertigo. I too have explained the feeling to my neurologist that after my "episodes" the next couple of days I feel "hungover"...and I don't even drink alcohol.
From my own physical experience with my migraines after they come to thee "end"..I feel very lethargic....I too have total concentrating and work hard to put the right words I'm looking for into sentences, and a variety of other ill feelings that make me feel I was on a bender!!. In my little "headache world" I think I have these ill effects because the migraines and vertigo get so terrible that it physically reaks total havoc on my body and this seems to be the same feeling I get when I'm coming "back" from a bad episode.
So...yes indeed...I can SO relate!!