Can I publish a map from ArcMap (Desktop) to ArcGIS online without belonging to a larger organization/ without a server URL? I am a freelancer and on my own in this great big world.
Unfortunately, you cannot publish content from Desktop to ArcGIS Online with a public account. However note from the following documentation: FAQ: Can a user with a public account publish hosted feature services to ArcGIS Online
"Users can still upload data to their ArcGIS Online account using their public accounts by exporting the feature classes as a shapefile and zipping it using Windows Explorer. However, only 1,000 features can be uploaded."