having an injury
In Italian, 'avere un infortunio' is used to describe the state of being hurt or injured, whether in a sports context, due to an accident, or in any other situation where someone experiences physical harm. It emphasizes possession of an injury, akin to saying one is currently suffering from a physical ailment.
I had an injury during the match.
This phrase expresses that the speaker experienced an injury while participating in a game.
After falling, he sustained an injury.
This sentence describes a situation where someone gets injured as a result of falling.
The injury he sustained forced him to rest.
This phrase indicates that the injury required the person to take a break from activities.