While that is true, each teen is still an individual person and each person's anxiety is intensely personal and just as real and serious to them as any adult person – except that teens don't have the life experience of getting through it to the other side. IME, that makes anxiety worse for teens than at any other age.
As for how I might have reacted, well… I would have been crushed. But, I think I'd have gone to my teacher and explained that I'd mistaken the timing and studied for the wrong exam. My experience is that most teachers are amenable to helping students they've seen do the work and try their best.
Of course, there's always that ONE teacher… we've all had that one teacher, haven't we.
Editorial note: There are a few places where your grammar and punctuation was incorrect. In your opening, you wrote, "my younger brother and I had to give an exam" – The teacher gives the exam; the student must take the exam.