His health is in question because Pike was killed in front of him. He was no doubt showing signs of general stress, PTSD, survivors guilt. Etc...
It's supposed to play into the notions of conflict being set up early on, and indicate that his state of mind is probably not what it should be to take on the mission. It's something that he slowly sheds as they get closer to the mission at hand.
that's what I thought first. but after frequent rewatching I got the impression that after bones got the test results he was even more worried about kirks health and it doesn't look like it was about his stress level