Flower Bug,
Do you realize that most barbell pieces of jewelry only have one of the ball ends threaded so it can be screwed off? Chances are you are trying to unscrew the end that is permanently fixed. If you have someone else take a close look (since looking at your own ears can be really hard) you can usually see that one end is permanently attached, where there is no gap between the post and the ball.
Another possibility is that you've worn this barbell so long, the end that unscrews is kinda stuck. You can use needle-nose pliers to grip the bar and then loosen the ball with a pair of flat-nose pliers (tape them to protect the jewelry from scratches).
