Considering that Brian was just in a plane crash and is now alone in the wilderness, he is both mentally and physically doing quite well.
That's not to say that Brian is injury-free. He's alive and has no broken bones or serious cuts. He is in a lot of pain though.
"He was still in pain, all-over pain. His legs were cramped and drawn up, tight and aching, and his back hurt when he tried to move. Worst was a keening throb in his head that pulsed with every beat of his heart. It seemed that the whole crash had happened to his head."
Brian has bumps and bruises all over the place. A few paragraphs later, Brian describes that his head is very swollen and so tender to the touch that he almost starts crying after touching it.
Mentally Brian is doing well too. He is obviously scared about the situation, but he never lets panic consume him. I'm not sure most people would be as calm as Brian is. He feels fortunate to be alive and remembers that the pilot wasn't so lucky.
In chapter 5, Brian remembers that his English teacher, Mr. Perpich, stressed the importance of having a positive attitude. Brian uses this memory to motivate himself to tackle the survival tasks at hand. Brian correctly assesses the situation and understands that rescue will not happen within a day or two. Brian also is clear headed enough to know that he must find/make shelter, or he may not survive.
For a 13-year-old kid, Brian is remarkably in control of himself. He forces himself to think short thoughts and analyze the situation piece by piece. Brian is able to focus and decide to concentrate on the things that he can control. That kind of thinking and resilience is what allows Brian to survive the entire ordeal.