I figured it out! I had defeated Clemont and gone to the cafe, but I must not have saved and lost power, so I lost my progress. Because I was in the city and not the wild, my Pokemon did not change levels, so it wasn't very obvious. I retraced my steps from the power plant back to the gym and noticed my name wasn't carved on the 'mysterious posts', checked my badges, sure enough, wasn't there. Oops. So I beat Clemont, again, and got my badge, again, and now well on my way on Route 14. Thank you all!!!