This swelling and discharge can have a lot of causes. First, he could have a bug bite or other allergic reaction going on. If this is the case, your vet might want to prescribe some benadryl to give him some relief. Second, he could have an eye infection or corneal abrasion. If the discharge from the eye is green or yellow, you need to go ahead and see your vet. Third, some parasites can cause eye issues so you should see your vet for a fecal to rule this out.
Eye health is very important so I would go ahead and see the vet with him.
Let me know if you still have questions.