Is it normal to have bloodshot eye after pink eye?

During & after. During "pink eye" people generally have red "bloodshot" eyes, and this can persist for a little while once you've treated the pink eye, but it should gradually resolve. If it isn't then you'd need to consider alternative causes of red eye (ex allergies, corneal abrasion, subconjuctival hemorrhage, blepharitis, dry eyes, others), and this may necessitate a trip to the eye doctor.