I think your turkey may have something like mine did a while back...our turkey had the same eye issue, snotty nose area, and was also gasping for air a bit.
turned out it was a respitory infection. We took him to the vet and she gave us something called Baytril. We had to give him a dropper full of this stuff (which was peanut butter flavored and smelled soooo good), twice a day, every day for about a week.
We also use VetRX, which we purchased from Atwoods. That'll be good if your turkey just has a cold. Get a wet cloth and wipe off the boogeys then put a few drops of the VetRX down his nostrils. Maybe rub a bit ontop of his head before he goes to bed. I also read that if you have too much trouble doing that, just put some drops of the VetRX into his water. When he goes to drink, he should get some of the VetRX on his beak and near his nostrils.
Also, I would REALLY recommend seperating him from the rest of your animals. When our turkey had this, it spread really fast to our chickens. It was a nightmare for us.
