Herpes virus infection of the eye can certainly occur! In fact it is a very common form of ocular infection especially in western countries where the incidence in the general population is significantly higher.
The infection can range from a skin infection, conjunctivitis, superficial corneal keratitis, deep immune-mediated keratitis, inflammation in the eye (uveitis both anterior and posterior), as well as retinitis causing retinal necrosis (in the form of acute retinal necrosis, or posterior retinal necrosis), or optic neuritis and other forms of encephalopathy / meningitis.
If you suspect that this is a concern for you, then emergent consultation with your attending ophthalmologist is an absolute requirement.
ESG