How do I upload a Featureclass to a Geodatabase in C#?

Given the details, you can construct a new feature class based on the details of your in memory object (IFields, etc)

You can view examples in the .NET ArcObjects documentation (http://resources.arcgis.com/en/help/arcobjects-net/componenthelp/index.html#//0049000000pz000000)

After creating it, you can insert each object. This is a painful/ineffective way, but it should work.

Another option that you have is to use the IGeoprocessor interface and IGPProcess, and execute a tool like append.

http://resources.arcgis.com/en/help/main/10.1/index.html#//001700000050000000

I think this could be accomplished more simply by using the Copy method of the IDataset interface.

Once you have the existing feature class (featureClass in your example) and destination workspace defined (pWorkspace in your example)

Use the following where "CopyName" can be changed to whatever you want the new feature class to be named ("al012009001_5day_linnn" for your example)

ESRI.ArcGIS.Geodatabase.IDataset dataset = featureClass;
dataset.Copy("CopyName", pWorkspace);