Wrestling is a high-risk contact sport. Points are earned based on how the wrestler pins his opponent. More points are given for difficult moves. The more difficult moves like the lift or the tackle have a greater chance for injury.
There are no statistics for injuries in young wrestlers. Adult wrestlers have about the same amount of back injuries as weight lifters, gymnasts, and soccer players. High school wrestlers practice regularly, even daily for weeks at a time before and during wrestling season. Training is important, but overtraining adds risk.
The best approach is to talk with the coaching staff about your concerns. Or better yet, go to a few practices and see for yourself. A good coach includes warm-ups, stretching, strengthening, and balance exercises. Safety should be stressed at every practice.