It is really terrible to get oil based paint in your eyes. Oil based paint can be poisoning if there are large amounts of and it may damage the eye and consequently reduce your ability to see.
But you just get a bit in your eyes, so you can try just wash it out.If it does not work well, go to see the doctor.
You should wash the oil based paint in your eyes immediately with the clean water. Then you could use the clean cloth to dry it. You could also use the warm compress to make your eyes feel comfortable. In addition, you could use the eye drops to release the symptom. The eye drops will clear the eyes and bright the eyes.
Well, generally speaking, for your situation, you can just have some solution to treat your eyes. First, you need to wash your eyes with pure water as soon as possible. And in that way, it will wash the oil out of your eyes. Of course, it may not wash cleanly. So in my opinion, if you feel itchy, red eyes, you need to go and see the eye doctor as soon as possible. Maybe he will give some prescription eye drops, which can be effective for your situation. Also, some cool teabags under your eyes can be tried. Anyway, just be careful about it.