Yes it is possible for this to happen, but it is not a common complication of the herpes simplex virus (HSV).
HSV type 1 causes cold sores, is very common and the type that usually affects the eyes. It passes to the eye the same way as HSV passes to other parts of the body by direct skin to skin rubbing with an area that could have the virus on it. You also need to be careful if you touch a cold sore not to rub your eye before you wash your hands.
Ocular (eye) herpes can range from mild to severe and in some rare situations can lead to blindness.
If you are concerned this could be happening to you I would suggest seeing your health care provider.
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