When your kids have pink eyes, the membrane will line the insides of the eyelids and cover the whites of the eye. In other words, it's an infection or inflammation of the top covering over the eye area. On the other hand, for bloodshot eyes, it spreads out under the white part of the eye causing a noticeable red patch. So you can just distinguish them in this way. Also, if you have pink eyes, you will have some symptoms such as itching, burning or stinging, discharge, swelling, watering. Some forms of pinkeye are contagious, and some are not. And bloodshot eyes can be caused by irritation, allergies, eyestrain, environment, wearing contact lenses, dry eyes. Anyway, you should take your kid to the hospital so that he can have an eye exam.