Nero did not consider himself prideful for having a high opinion of himself. The distinction between confidence and overconfidence is that confidence is based on empirical evidence and historical proof, whereas overconfidence is based solely on emotions.
Nero had, time and time again, proved himself to be exceptional in various fields. He also had countless advantages over others, which included the fact that he was highly disciplined and strong willed.
With that background knowledge, it was a fair estimate to say that Nero would be able to handle himself better than others in a given situation. In the case of pain, especially, he was confident, for he exposed himself to great pain every time he trained.
Not only was it extreme physical exhaustion that he subjected himself to, but there was also the emotional equivalent of forcing himself to do things he knew would hurt, only for a long distant dream or goal he had no way of knowing he would ever achieve.