Chris,
Any user with the necessary permissions can add data into a geodatabase. You don't need to be the owner of the geodatabase to add new Feature Class.
If you currently don't have permissions, then YES, you need to contact that person and have him grant the permissions.
NOTE: It would be really great, if you post details of the version of ArcGIS and Database you are working with, along with the original post, so that we can provide you with any related links which would help.
Regards,