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Hi there. Is the swelling constant or does it come and go? Is there any redness relative to the other side?
Can you upload a picture of the eye?
Carbuncle implies an infection under the skin. If you had this I expect that your eye doctor would have treated it. You might have a chalazion. This is also called a meibomian gland lipogranuloma, and is a cyst in the eyelid that is caused by inflammation of a blocked meibomian gland. They can be chronic and can enlarge. If creams and compresses dont work, as a last resort, surgery is performed. The eyelid is injected with a local anesthetic, a clamp is put on the eyelid, then the eyelid is turned over and an incision is made on the inside of the eyelid, so that the chalaion can be drained and scraped out with a curette. If the previous ophthalmologist was not willing to do this, you should get a second opinion. You might seek the advice of a plastic surgeon this time.
That's why I asked for a picture. :-)
At any rate, there is often asymmetry in the caruncles. When one is enlarged it usually indicates that it is more susceptible to an allergen in the environment. Does it shrink at all with oral or ocular antihistamines?
If there is no change with antihistamines, I would seek a second opinion, preferably from an ophthalmologist at an academic medical center (i.e one with a medical shool). They are typically at the cutting edge of their field and should recognize anything out of the ordinary.
The most common non-allergic causes would be nevi, papillomas, and sebaceous gland hyperplasia. Excision of such lesions is indicated only if there is an atypical presentation, a carcinoma is suspected, if mass effect causes discomfort, or if cosmesis is an issue.
I would definitely have it looked at by another professional.