For the eye, I would flush it with some warm saline twice daily and blot it dry with a clean towel very gently. If this is an allergy or a foreign object in the eye, this will help. If the discharge turns to green/yellow, you will need to see your vet right away.
We really don't worry too much about hicoughs. They have them for the same reason that people do in most cases and this means no discernable reason at all.
Let me know if you still have questions.
