Is it possible to get herpes around your eye area?

Yes. Type 1 HSV is more common around the eye. This is the same virus that causes cold sores. It behaves like any herpes virus with recurrences, and if it involves the eyeball or cornea can lead to serious vision loss.
Yes. One can definitely get a herpes viral infection around the eye. This is a serious condition that needs to be properly diagnosed and treated by your physician or ophthalmologist as an untreated infection can lead to corneal clouding and blindness.