While it is impossible to make a diagnosis with certainty without seeing you, this sure sounds a lot like dry eyes.
Allergies itch, infections don't last for years, and rosacea may be a contributing irritation but the long duration as well as the eye specialist's conclusion all point at dry eyes as the problem.
Dry eyes cannot be cured but they can be treated effectively. We generally start with artificial tears and other lubricants which give temporary relief and are all that are needed for mild cases. To this we can add a nutritional recommendation for high levels of high quality omega-3 and fish oil supplements by mouth. Another measure that can increase the amount of your own tears is cyclosporine drops which are prescribed by your eye specialist. Finally, very tiny (punctal) plugs can be placed in your tear exit ducts on your eyelids to increase your own eye lubrication.
If you have co-existing rosacea, an oral tetracycline type medication can be prescribed. If you have dry mouth as well as dry eye (as well as certain forms of arthritis) Sjogren's syndrome should be suspected and can be confirmed by special testing.
Again, dry eyes cannot be cured but your life can be made a lot more comfortable by one or more of the above measures.
Best idea, especially considering the severity of your symptoms is to find an ophthalmologist who is a definite expert in treating dry eyes. Start at
www. AAO.org and pull down the "Find an Eye M.D" tab searching for a "Corneal/External Disease" specialist in your area.