We are making a piece of software that lists some kind of objects. An object may belong to a user (be 'private') or it may be made 'public'. The list is quite large, therefore in the list form there's a filter panel. One of the controls on that panel is the 'Privacy' drop-down box with three options: 'My only', 'My & public', 'All'.
However, this usage of a possessive determiner without a noun seems dubious to me. Wouldn't it be better to use 'mine' instead of 'my'?