Dan,
Ulnar nerve pain is most certainly NOT normal.
It means that you have a mechanical problem that is placing extra strain on your elbow.
One thing to check is the angle of your pitching arm side elbow, and the position of your pitching arm side forearm, at the moment that your shoulders start to turn. I'd be willing to bet that you are turning your shoulders before your pitching arm side forearm is vertical. Your elbow might also be bent more than 90 degrees at the moment that your shoulders start to turn (so that the ball passes closer to your head). Mark Prior does this and it is one of the causes of his elbow problems.
One thing that you might want to work on is pronating your wrist as you release the ball (turning your wrist counter-clockwise so that your palm faces the ground). This will take some of the load off of your elbow.