As far as I know, eyeliner is made up of chemical substance which is quite irritate to human beings. Therefore, direct contact with your eyes would do extreme harm and cause uncomfortable feelings. Yes of course it irrirtated your eyes. For now, you need to flush your eyes with some hot water. Afterwards, try to get some eye drops with the help of the doctor. Follow his advice and do it now!
Yes, eyeliner can irritated you. I think you should change your eyeliner right now, and buy a new one which is mild and with organic ingredients. I recommend skin food products and clinique to you, because those are mild and suitable for the people who are easy to be infected. What's more, you must recap after using them to avoid bacteria from going into them.
Some people just have more sensitive eyes than others. What types of eyeliner do you use? If you use pencil type, then you need to wear creamier eyeliner to have a try. Besides, there is eyeliner at walmart called black radiance I use their cream eyeliner and my eyes don't water and it lasts a long time like 5 hours. If you're using the creamier eyeliner, maybe you can try "rimmel london" which makes really great pencil liners that aren't cheaply made. If both of them don't work, then maybe you are allergic to eyeliner. In this situation, you should give up eyeliner in order to keep your eyes healthy rather than make them look bigger.