Bright red eyes in a photo, could it indicate a medical condition?

No: The red eyes in photos is a reflection of the flash off of the retina. However if one eye is red and the other is not, there could be an eye problem present.

Normal: This is a common and normal phenomenom (red reflex). That's why there is a "red eye" feature on most digital cameras. You probably have large pupils. If the color of one of your eye reflexes was white (leukocoria), that needs immediate investigation.