Red veins can be seen in the sclera or the white portion of the eye, which can be caused by various factors. Firstly, you are affected by inner factors, such as too much stress or trauma, could be one essential factor. And you extensive use of contact lenses to make scratches in the cornea, dry air irritate your eyes, or you exposure prolonged time under sunlight. Those external factors could lead to prominent red veins in your eyes. On the other side, it could be a sign of some serious eye problems, such as glaucoma.
Well, you don not need worry about it. The veins are normal and they happen in every people's eye. It may just appear more prominent in some situation. If they occur to your eyes, you should take some measures to treat them. For example, if you are having any dry eyes, some lubrication eye drops may help. Also, you should drink more water so that it can relieve the symptoms or just have good rest so that they will go away.
If there exists the red veins in your eyes, your eyes must be dry because of the long use in front computers or using eyes on other aspects. You'd better have a good rest for the eyes, in case of the bad infection which cause the eye disease. You can eat more food with vitamin C to moisture the eyes.