Hi thanks for your question.
Breathlessness, pain and pressure over chest after a jump from diving board could give rise preumothorax that is air in pleural cavity
(chest). This is the No. 1 possibility which comes into my mind.Though pneumothorax
is medical emergency, but mild pneumothorax can give rise to this type of symptoms without any danger. Examination by a physician followed by investigation like chest X-Ray is necessary to rule out this condition, which if present needs ER treatment. The other possibility could be trauma to chest wall or back.
Hope this answers your question.