Yes, it is very normal. Dust mites are very common in human accomodation. They are almost everywhere, in your pillow, quilt, carpet, cushion and furniture. They are invisible to human eyes, but if you use a microscope to look carefully you can find them. Dust mites are proved to be typical allergens, including its excretion, secretion and decomposer of the dead mites. Excretion of dust mites has the strongest sensitization. It would cause runny nose, itchy and watery eyes, asthma and allergic rhinitis. I think you should wash your eyes with water immediately. Minimize your exposure to dust mites would help a lot. Make sure wash your bedding clothes with hot water every two weeks. Insolate the pillows and quilt under sunshine if possible and flap them. Better not to use any carpet in bedroom. If your symptoms still linger, you should visit a doctor at your earliest.