one of the biggest factor with sport related injuries is balance. When you use a particular set of muscle repeatedly, strengthening those muscles, the opposing muscle often gets neglected, and this throws the body out of balance. Just think for every direction you can turn a joint, there is a muscle opposing in order to turn that joint back again.
Do pushups, curls (not just the 12 oz variety) and pilates. Also vary the style of climbing, don't just face climb, crack or just steep climbing.