A brain thorn is, simply enough, something that gets stuck in your head. Not literally, of course (Claire does NOT get brain thorns). More like a "What was the name of that guy from that show where Phoebe from friends played a waitress?" kind of something. (Answer: Paul Reiser. Or maybe Hank Azaria?)
I also suffer from a tendency to mentally relive - over and over and over - problems and questions and happy memories and funny stories and everything else in the world.
Anyway. I have these issues often, and I've found that writing this stuff down can short circuit said issues (yay!), which is infinitely better than worrying at them like a sore tooth.