You might consider using essential oils for earaches and ear infections only if the problem is in the external ear canal. Middle or inner ear infections require professional attention; consult a doctor as appropriate to avoid possible damage to the eardrum.
Potentially effective essential oils include:
Select an essential oil and dilute a few drops 50/50 in carrier oil. Massage some of the blend around both ears (even if only one ear aches) every few hours. Also massage the ear lobes.
For a synergistic effect, make the following blend for massage:
Here's another possible massage blend:
Source: Essential Oils For Healing
For children, you can make a warm compress:
After using the compress, make a blend of:
Dab a cotton ball in the blend. Gently place the cotton ball in the ear, replacing it with a new cotton ball three times a day.
Source: Healing With Aromatherapy
For ear infections in adults, blend:
Massage the blend around the outside of your ear and down your neck.
For children, use only four drops of each essential oil in the olive oil. For infants and toddlers, blend only two drops of each essential oil with the olive oil.
Source: Aromatherapy for Dummies
An alternative blend is
Again, for children, use half the amount of essential oil.
For best results, use these blends around both ears, even if you have pain on only one side. Continue using the blend for several days after the pain goes away so the problem doesn't return.
Also, a study on treating acute otitis (ear infection) in rats found basil essential oil (Ocimum basilicum) effectively got rid of infections. You can try diluting basil in a carrier oil and massaging the blend around the outer ear (dilute more for young children).
Related: Essential Oils For Colds