Eye irritation can be caused by several reasons. According to what you said, I think you may be affected by allergies. When something irritating (allergen) invades your eyes, like dog hairs, cat dander or fumes and so on, your eyes may feel irritated. It is best to seek the opinion from an eye care professional. If this is the reason, you can cure it by avoiding touch the dogs.
Before you know more about what caused your problem, you should avoid rubbing your eyes. You should wash your hands often. And use cool, wet compresses on the outside of your closed eyelids for relief. If the irritation continues to annoy you, you have to see your eye doctor for a prescription to help you solve your problem.