Without question, I would have a vet examine him. Any injury resulting from a paw, tooth, etc..during a fight can easily become infected, despite you cleaning and applying neosporin. He should really be on oral antibiotics, as well as, an appropriate topical medication that is safe to use near the eyes.
In addition, with an injury that close to the eye, if there is ANY redness to that eye, absolutely it needs to be evaluted for a corneal ulcer (which usually you can't even see with the naked eye).
Well worth a veterinary examination.
I wish I could answer. Without being able to see the eye and the cut myself, I can't make that judgement call.
You can use this link to help find an ER vet in that area:
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