Saying that someone has their "head held high" is a common idiom. It means that they can be proud, they have nothing to be ashamed of. When he says "he got in his own head" I'm assuming that he means he took some time to reflect and collect his thoughts. But this isn't something that's commonly said.

"Getting in your own head" means to overthink or overanalyze a situation so much that you clutter your own mind or get nervous and confused and cannot think clearly. "Head held high" means to be confident and proud of yourself. Hope this helps.^^