Joe,
If you have an organizational account, you can upload your layer as a feature service, which maintains your symbology. You need to do the following.
Open the MXD in which you have prepared your layer with your symbology. Make sure only that layer is in your MXD.
1) Click on File -> Sign In... (Here you sign into your organizational account)
2) Click on File -> Share As -> Service -> Publish a service
3) As connection choose My Hosted Services (My Account) and as service name use what you want the layer to be called.
4) Under the capabilities tab uncheck "Tiled Mapping" and check "Feature Access"
5) Fill out the Item Description tab
6) Under sharing you can check who is able to see it once published
7) Click Publish in the upper right corner and it will soon show up in your "My Content" on ArcGIS Online
Hope this helps!
Tim