When you get an oil burn the first thing you should do right after getting the oil burn is to run some cool water over the oil burn.
Run the cool but not cold water over the oil burn for at least 20 minutes.
After you run the cool water over the oil burn for 20 minutes then you can apply a cool compress and some Aloe Vera gel or even some honey to the oil burn.
You should wrap the oil burn in some gauze and apply some antibiotic ointment to the oil burn until it heals fully.
Oil burns usually heal up within 3 to 4 weeks.