How can protein help injury healing and rehab?

Yes, but.... A 'normal' diet is critical for proper healing and rehab. The answer to needing a protein supplement is probably no. Just be certain to eat a balanced diet and you should do well. If you have a diet that does not incorporate meat proteins or a decreased protein intake then you may need to supplement. Have fun and get better.
High BMR in injury. The body needs a certain amount of nutrients to maintain a constant, healthy state. This need is determined by the basal metabolic rate. Any external or internal trauma raises the metabolic rate, and greater amounts of oxygen and nutrients are required to supply enough fuel and Amino Acids for repair and recovery. Energy expenditure may rise by 10 percent to 50 percent to support high bmr.