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I suggest that you take him off the hay completely if you can. If you can't you need to at least soak the hay or spray it with water before you give it to minimize the dust that the horse inhales as he eats.
These allergies are usually a sign that the hay has some sort of fungus or is "dusty." Many horses have these symptoms after being exposed.
Most horses will get over this on their own after 7-10 days. If the horse is not eating well or seems to be distressed, you need to give a call to your equine vet.
If your horse has a problem with allergies, you should also talk with the vet about an antihistamine that you can have around in case this happens in the future.
Let me know if you still have specific questions. I would be happy to help more.