I don't think the HSA would appreciate every minor or even medium cut , graze, bump , bruise been reported to them. There are legal requirements to report , 3 day lost time, amputations, fractures of long bones, blinding, death. to HSA, however the smaller stuff must be reported internally in a company or there will never be improvement.
The nail is gone, there was first aider, it wasn't stitched so unlikely to leave a disfiguring scar. As this has happened to you , why don't you offer to take on a safety role in your job?, safety rep?.