In fact, your eyes are not turned red when you take pictures. Your eye appear red in the picture because the flashes, or "the pumpkin". When the flash from cameras is too close to the lens, the blood in the back of the eyes can reflect straight back to the lens that make your eyes appear red in photos. It is not a big problem. Don't worry.
Don't worry, it is not a problem of your eyes. It is the light reflecting off the retina that cause the red look in the eyes. In common the relfection in the retina can be caused when the flash is too close to the lens. Or the red eyes in the photos may caused by the Red eye mode in your camera. You may forgot to turn on it. So, check your camera if you find red eyes in photos.