Is arriving at the examination center unimpeded a sign that God chose that for me, despite my inner feeling of unease about taking the exam, or should I have obeyed what was in my heart and left the examination hall, and was what I did correct?

If you have performed the Istikhara prayer, then proceed on your way without hesitation; for what Allah makes easy for you is what is good. There is no harm in traveling on Friday before Zawal (midday), and this is the most preponderant opinion among scholars. As for after Zawal, the majority of jurists prohibit it except out of necessity, such as fearing the loss of companionship or an exam.