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Eyelid chalazion can be permanent. They can be removed whether causing irritation or just a cosmetic problem. They are best removed from behind eyelid approach. See following link and video.
If a chalazion has not gone away on its' own after 2 years you will need surgical removal. Go to another doctor.
A chalazion is essentially a clogged oil gland along the lash line. These usually resolve on their own, but sometimes the chalazion encapsulates itself and becomes more of a cyst instead of a stye. Since yours has been there for so long, it is most likely cystic and should not be considered cosmetic. That being said, without a consult one cannot be sure. I would suggest seeing an oculo-plastic surgeon, which is an ophthalmologist with a concentrations in plastic surgery specifically around the eyelids, about your concerns to discuss possible options for you.