Do I have to register my copyright if I have submitted a pre-registration to the U.S. Copyright Office?

Yes, normal registration upon or after publication is necessary even if you have pre-registered your copyright. A work can only be registered once it has been published, and conversely, a work that has already been published cannot be pre-registered. A valid pre-registration does not automatically become the registration for the work once it is published, so it is necessary to obtain the registration to continue to protect your work after publication.