What Causes Bleeding From The Corner Of Eye?

My son age 16 has blood coming out of the corner of his eye. It is not a lot and is not constant but has been going on for about 6 hours. He has a cold and will get bad nose bleeds from time to time. Someone had said that this could be a broken blood vessel in his nose that can only get out his eye because of a stuffy nose due to the cold. So I guess my question is do you feel that could be true