Yes, it is possible to cause bloodshot eyes because of virus. virus can cause recurrent viral infection thus cause to bloodshot eyes. Besides, other factors such as allergy, eye injuries, pink eyes contact lenses wearing, computer vision syndrome can also cause bloodshot eyes. In addition some eye diseases such as corneal ulcer, glaucoma and uveitis can also be the factor of bloodshot eyes. So, don't ignore your eyes if you notice that they appear bloodshot. Treat it immediately if you got bloodshot eyes caused by virus.