Homeopathy does offers certain medicines for swelling under the eyelids or around the eyelids. Medicines like Kali carb, Apis, China are often used. But the success of treatment depends on conditions like whether the swelling is oedematous in nature, or there is collection of fat, or there is lax tissue, or if this is a hereditary feature. If the eye bags show any variation in size with the day then they have a much better prognosis with homeopathy.