Hi, you can add fields in the properties, in ArcCatlaog.
Alternatively, if you're game, make a copy of your shapefile, then open the .dbf table and save it as an Excel spreadsheet. Cut and paste and add what you need to your table, making sure you adjust the field types in Excel and save as Excel. then Save as .dbf using the same name as the dbf table in your shapefile and replace the original one.
If this doesn't work, you can always go back to your copy.
But ... ALWAYS make a copy first ...