This is a very normal reaction for a coach and not a bad reaction. You are anxious and worried because yiu are a coach who cares about your gymnasts and cares about your coaching.
We can’t go back and prevent an injury fro happening, but we can use it to help ourselves grow as coaches. Obviously we don’t know the nature of the injury but you can look back on the incident and ask yourself, what could be done to prevent such an injury occurring again. Some possible ideas.
1. Including injury prevention training in their lesson plans, especially for their joints - wrists, ankles, knees, elbows, shoulders, hips.
2. Increase the gymnasts strength, stronger gymnasts are less likely.
3. Have a better system for evaluating strength, to ensure each gymnasts strengths and weaknesses are being developed.
4. Increase gymnasts flexibility. Better flexibility also reduces many injuries.
5. Improve the safety of the facility. Are there places where you should be matting the wall, having better matting on the floor, have apparatus too close to another apparatus, have ripped or torn covers on equipment etc.
6. Introduce new equipment to teach skills more safely - Pits, spotting harnesses, inground bars bars, beam mats etc.
7. Improve the progressions for skills. Look for more drills and better ways to teach skills so they are very solid before doing them in a full competition type situation.
8. Look for signs of a gymnast who might be heading towards an injury - looking tired and lethargic, losing focus, skill starting to go off direction, losing body tension etc.