The major reason I would say go to the ER is because the OP can't just rush to the vet early the next morning because this was a Saturday night.
A vet needs to look at the eyebal, look at the wounds, clean out the wounds, prescribe antibiotics, and assess the situation and tell the owner what to watch for.
None of these things can be done from home and none of them should wait.
Bite wounds can also be much deeper than they appear and the OP could have easily missed areas under fur.
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