Hi,
The answer is that your layers do not show up in MyContent because they are not services.
ArcGIS Explorer Online can only load data which comes from ArcGIS Server - namely map, image and feature services. This type of data is always accessed by a Url. At present to create one of these services you need to have access to an ArcGIS Server.
To answer your specific questions:
- A .lyr file is a file that represents everything to do with a layer - it's name, scale thresholds, labelling, the symbology it is displayed with etc. The data source itself could be any number of things - shapefile, geodatabase feature class, ArcGIS Server map service etc. ArcGIS Explorer online cannot load .lyr files.
- Unless http://datawarehouse.hrsa.gov serves the data as ArcGIS Server services you will not be able the data to ArcGIS Explorer Online
Esri is actively working on providing a solution which will allow you to create a service from your data (e.g. shapefile, csv file etc) without having to actually own ArcGIS Server. This process has been demonstrated at a number of conferences recently but it is currently still under development and there is no release date for this as yet.
Mike Rudden
Esri