Brent, behind the eardrum is the middle ear. Amoxicilin should take care of a middle ear otitis pretty well. In the worst case infection will end up perforating the drum and suppurating, which would relief the pain. However there's probably some inflammation of the external ear canal. If symptoms worsen, like more pain, dizziness, vertigo, hearing loss, facial palsy... go to your ENT right away.
Take your pills, use some local heat on your ear, and avoid water getting into it, just the antibiotic drops. Feel free to PM me if I can be of any assistance