In cases like this the question is whether the irriation around his eyes is being caused by something external or internal. For example, dogs who come in contact with substances that irritate the skin on their faces may rub the area with their paws or on carpeting or furniture and wind up irriating their eyes, too. But it can also work the other way: adog can have an infection of the soft tissue around the eye, i.e. conjunctivitis which causes the dog to rub or paw to the point that it irritates the skin around the eyes.
A third possibility is that something could be going on inside the eyeball itself, such as a build up of pressure, that causes discomfort. This could also cause a dog to rub and, depending on where or how the dog rubs, this could produce both a secondary infection that causes discharge and irritate the skin around the eye.
In all cases discomfort and/or infection may make a dog less interested in eating. Given the obvious discomfort your dog is in, I suggest you get him examined by your veterinarian asap.
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