Not necessarily normal, although HRH has bloodshot eyes and apart from her dry eye we are treating its normal for her.
It could be as simple as an allergy symptom or something related to a more serious eye condition.
You should make an appointment to see the vet. Just to be on the safe side and rule out anything serious.
Could just be from allergies but as [MENTION=983]LariP[/MENTION] said it could be something more serious, so if it continues you may want to check with your vet.
I don't mess with eyes..could be allergies or something but I know that when mine would get excited they would be a little red. Of course, it was gone after they calmed down.