When you wired the bumper light wires, are you sure you wired them to the correct power wires? Also, is this a 3rd Generation Integra (94 - 01)?

If those 2 wires you wired together are truly ground wires, it's fine if you wired them together, but you still need to ground them onto the car's frame or to another ground wire. I'm not sure if the 2 wires you wired together are both from the lens assembly or 1 ground wire from the bumper light and the other ground wire from the car's electrical system.