Yes, it is true that milk can help people with irritated eyes. Irritation can be caused by swimming in the pool, or chemical conjunctivitis. And the antibodies in the milk works well on infection. You can use an eyewash with warm milk which can soothe and treat your infection. What's more, pollen and dust mites can also help your irritated eyes.
Because milk offers natural antioxidant which helps with preventing oxidation of cholesterol. Meanwhile, we also can get natural antioxidant from fruits and vegetables. Well, drinking milk every night when you go to sleep. Good sleeping can reduce eye irritation and milk will offer some supplements for your eyes when you are sleeping. And the most important factor is that our body can absorb some minerals faster at night. You also can wash face with milk in the morning that can smooth your skin, especially the skin around your eyes. However, this is a slow way to heal irritated eyes. Visiting a doctor should be your best choice. Irritated eyes are related to burning eyes and some other eye problems, so call a doctor for help, then you may recover soon.
Milk is supper moist and mild, it can calm the irritated eyes 99% for sure. If you have internal thermal, it may not be helpful for you.
Anyway, it's worth trying. Soak your eyes with milk few seconds, then wash your eyes with pure water or physiological saline. Make sure there is no deposit remain in your eyes.
The best choice for you is using professional artificial tears. It's the safest way as well.