I do a lot of work with that data, and one of my internal customers uses a simple spreadsheet to track their cases.
For the most part, a single spreadsheet page can handle most needs, of course, there are a lot of commercial relational database products out there.
Generally, you are going to do a one line per event listing. Date of injury/event, Description, Classification (such as First Aid, Medical Treatment), Owning Organization are basics. If you are going to use your spreadsheet to support OSHA reporting you'll need no. of days away, restricted, cause, and other descriptive fields on the OSHA 300 form.
An important thing is to set up data validation pick lists in Excel, so that there is a standard set of body parts, causes, injury types to choose from for the appropriate fields.
One limitation of a single page file is some fields may need multiple entries, such as multiple body parts may be affected in some injuries. If you intend to chart the data, working with the data analyst for how to handle that structure (Multiple body part columns, or separating the entries with commas) is needed. One of the most time consuming parts of analyzing the spreadsheet I get is programming the logic in for new body part combinations, and mispelled items, so they will count into the proper charts.