Yes, your eyes may suffer irritation due to dust mites. Dust mites are induced asthma allergic rhinitis and allergic diseases such as eczema important allergen. After you get allergic, the dust mites will affect your eyes which will make your eyes feel dry. You need to use some eyes drops with anti-inflammation to get rid of bacterium in the eyes.
OK, from what you said, I can see that you are quite allergic to dust mites, which is one of the most common sources of allergic reactions in the world. And I still remember I used to get infected because of that annoying stuff, which gave me a lot of troubles. Because it triggers some nerves in your eyes and nose, leading to some Allergy symptoms. Now you just need to see a doctor and follow his advice and pay attention to your eye health.