Well, as you can see peppermint oil is quite irritative to your eyes which could lead to some serious problems if not coped with properly. So, for now, you must not rub your eyes however terrible you might feel. Next, you gotta wash your eyes with plenty of salty water. Afterwards, you had better get some special eye drops to help under the doctor's advice. Hope you recover in no time.
You must feel some burning in your eyes. Don't be so worried. I think flushing the eye with lots of water initially would be important. You can use a carrier oil, like olive oil, on a cloth to wipe your eyes, and then wait for the burn to wear off. You would be better according to the following suggestion.
It is really terrible for you to get the peppermint oil in your eyes. You'd better wash it out with the clean water as soon as possible. You could wash it until you see nothing of oil in your eyes. Then you could use the warm compress to make the eyes feel comfortable.