It does sound like a chalazion (the common term is 'stye'). If it has persisted for close to 6 months with no trend towards improvement, the most efficient treatment is surgical drainage, which is a simple procedure that is performed in the ophthalmologist's office. As a conservative measure he can treat the chalazion with an effective hot compress, which is not a warm washcloth. Put about 1/2 cup of uncooked plain white rice in a pantyhose foot, tie a knot, cut off the remainder, and you have a rice baggy. Microwave for 20 - 40 seconds depending on the power of your microwave. Apply as a hot compress 2 - 3 times per day. The rice should stay warm for at least 3 minutes - if not, microwave longer. This may initially increase the tenderness as the impacted secretions liquefy. You can reuse the same rice repeatedly.
I think it's probably a chalazion. They're fairly common. They can be perfectly painless but can also become painful. An eye doctor can take care of it either by excising it out or giving it a steroid injection.