For what it's worth, I had a pig who developed corneal ulcers very late in life. The opthalmic antibiotic my vet prescribed was a thick paste ointment, so that she couldn't shake it out of her eyes. I'm not sure if a liquid drop would be helpful to a pig, even if the antibiotic is ok for them. I've never heard of that antibiotic and have no idea if it's safe for pigs or not, perhaps someone else would know.
What wouldn't hurt is rinsing the eye out with sterile saline. That ought to be perfectly safe for your pig (though he's not going to like it one bit). If there is anything stuck behind the eyelid that you might not see at first, it might help rinse it out. It also may not help at all if there is an infection. But it should not hurt, at least.