It depends. Sometimes, the red veins in eyes are normal. Besides, the red veins on the whites of your eyes don't necessarily impact your vision. Usually, red veins are result of lacking of sleep, a very tiring activity and excessive heart stimulation. Besides, it may be caused by irritation, allergy and infection etc. If so, you'd better visit an eye doctor
It is not normal to have red veins in your eyes which mean there is something wrong with your eyes. You could find that your eyes will not feel comfortable. Your red veins may be caused by the lots of use of eyes in front of the computers or other electric products. You'd better use some eye drops to release the symptom.