I think you should ask someone to help you first. Second, ask someone to wash his hands and open your eyelids to make sure where the dog hair is. If the hair is in the corner of the eye, you can ask him to draw it out with his hand. Otherwise, you can only apply eye drops or tear to rinse it. Third, remember don't rub your eyes whatever you do. Fourth, if you have pain in your eyes and feel worse condition, you should go to see a doctor to examine your eyes.
There are some methods for you to get the dog hair out of your eyes. Firstly, please do not rub your eyes after it's happening to avoid the bruise of your corneal. You can close your eyes for several minutes, if the tears will rush it out, you can wink your eye, and the foreign body will rush out of your eyes. If it can not work, please prepare a basin of clean water and put your eyes under the surface of water. rink your eyes for several seconds, the foreign body will go out. The last way, is use cotton swab or clean handkerchief soaking in the cold boiled water, then sweep it softy out from your eyes. Don't rub your eyes by hands, for the sake of avoiding infection by virus. After the dog hair out, adapt some eye drops to prevent your eyes from infection.
Well, it seems that you have some real trouble now. Because you should understand, sometimes dog hair is the breeding ground for bacteria and parasite. It would be quite dangerous if your eyes are not properly taken care of. However, if you start to have some allergic feelings, then probably you have got infectious eyes, then you need to visit a doctor before things get worse.