I'm using an ArcGIS Online public account to create some test Web maps. I've successfully imported .CSV data via the 'Add layer from file' option in a Web map, and Shapefile data (as .ZIP files) via the 'New item' option in my 'Content' page, along with several other data types (see 'My Content' page list, below).

If I try to create a new map and select 'Add - Browse Layers - My Content', I don't see any of my .CSV or Shapefile data from listed as options, just the other data types I have imported (Feature Layers, KML, GeoJSON, WMS) (see below).

Note the .CSV data sets work fine when I add it via the 'Add layer from file' option in the Web map, but I don't want to have to keep re-importing the same data set to add to different maps, creating multiple versions in 'My Content'.
Is this a restriction on a public account, or am I doing something wrong? I'm thinking about upgrading to a paid-for subscription, but only if I can be sure this works.
Thanks!