Layer packages can only be uploaded and downloaded for desktop use. They can't be added as layers to a web map. You're basically just using online as a file storage system.
When you add a shapefile or CSV to My Content, you have the option to publish it as a feature layer (hosted). This layer can be edited online and you can set symbology and other properties. If your idea is to update your local shapefile and post it back, that won't work, as you will need to wipe out the feature layer, thus losing your symbology. THe assumption with this workflow is that your feature layer online *is* your most current data and you store it online. Any client, like arcgis.com or desktop can edit the online layer directly.
If you want to maintain your local data on your computer as the main source and periodically push it online, I think this workflow may work for you. You can publish data from desktop, which also creates online layers, via the file menu, share as option. Here, you author a map with layers in it. Arcmap lets you define symbology for the layers that will appear online, and as long as the symbolgy is supported on the web (e.g., not complex multi layered symbols). This may be an option to explore, as the publishing process does have an update option. It still wipes out the existing layer online, but because you have the symbology defined in arcmap, it should transfer up to arcgis online. I've personally not used this workflow much, so I'm not an expert in this area.
Hope this helps,
Mike
