We learned from a Catster friend that she has a kitty Tina has one eye that tears constantly, which she never has to treat, and one that does not tear enough. That is the one she has eoinsiphilic keatitis in....a herpes-related issue. She uses the GenTeal severe formula in that eye. You can get it at any drug store.
Of course this advice should not be used other then advice and a vet should be contacted if the problem persists as dealing with eye issues with FHV should not be treated lightly.