Once you have the database setup, all you need to do is add the following to the <elmah>
section your web.config to setup the Elmah to log to the SQL Database:
<elmah>
<errorLog type="Elmah.SqlErrorLog, Elmah" connectionStringName="<DBConnString>"
applicationName="<YourApp>"
</elmah>
Replace <DBConnString>
and <YourApp>
with appropriate values for your configuration.
Once you have done this you will not need to use your custom ElmahHandleErrorAttribute class.
I am not sure which NuGet package you installed, but I would recommend using the Elmah.MVC package as it integrates Elmah into MVC exceptionally well by setting up all of the ErrorHandlers and ErrorFilters for you.