An earache is most likely due to an infection. While this is not the sort of condition to treat exclusively with aromatherapy, an aromatherapy massage oil rubbed on the outside of the ear is an excellent adjunct to other treatments.
For this aromatherapy treatment, dilute an antiseptic essential oil like lavender or tea tree in olive oil. Lavender has the added benefit of helping to reduce inflammation. Gently rub this around the outside of the ear and down along the lymph nodes on the side of the neck. Do not put it inside the ear itself. Instead, make a warm compress using these same oils and place it directly over the ear.
Always treat both ears, even if only one hurts, and continue treating them for a couple days after the pain is gone.
Essential oils for earache: lavender, tea tree