If it's under his eye rather than in his eye, it's not an emergency. It's most likely either a bacterial or a fungal infection. Fungus infections are very contagious, so treat it like it is one even if it turns out to be something else. Wear gloves when handling him, and change clothes afterward.
If it's really under his eye and not in it, then I'd start out by getting some Monistat or Lotrimin and putting a dab of it on with a Q-tip. Rub it in well. Do this a couple of times a day for a few days and see if it improves. If so, keep on with that treatment until at least 5-7 days after it looks like it's cleared up.
If it hasn't improved after a few days, then get a triple antibiotic cream and treat with that instead.
One or the other of these treatments should work. The symptoms of fungal and bacterial infections are very similar, and it's hard to tell which is which. One not-totally-reliable test involves a skin scraping, which is painful for the pig, especially close to the eye. But if you treat for a fungus first and it turns out to be a bacterial infection, the fungus treatment won't make it any worse even if it doesn't help. If you treat for a bacterial infection first (the antibiotic) and it's really a fungus, the antibiotic will make the fungus get worse very quickly.
Good luck, and let us know how he gets along.