It sounds like you may have more than one file to your database. That would explain "There are no tables or fields listed when either of those tabs are selected."
To update your value list, you need to find a layout that lists the contents of Options table and which displays the Category field. If you use that layout to add a new record and type in your new value for Category, you'll get this fixed.
If you can't find a layout that works, you can make one easily.
Enter layout mode.
Select Layouts | New Layout
Select "Options" as your "Show records from" table
Select "Table" as your layout type
Click "Move all" to add all field from Options to your layout
Choose "Default" as your layout theme
Click Finish to dismiss the wizard and you should now see a table view of Options that you can use to edit values in that table.
Your Value List is built from a field in table and, therefore, the only way to add new values to your Value List is by adding a New Record for each new value.
If you have a Layout for the table Options just go to that layout and add a new record and insert your new value in Options::Category.
If you don't have access to a layout for the table OpTions, you can create a new layout just for the above purpose!
Let me know if I misunderstood your issue, or if you need further help.