No, you can not use essential oil to cure your eye stye and it may make the condition worse. Eye stye is a kind of acute purulent inflammation in eyelid gland and eyelash follicle. You should go to the hospital for treatment in time, or else when the conditions get too serious and begin to have ulceration, the eye stye may leave scars on the eyelids. You should use antibiotic eye drops to cure your eyes. If necessary, an eye operation may be needed. In addition, you should pay attention to your daily diet, do not eat too oily foods and as well pay attention to eye hygiene work. Besides, have good rest.