My right eye has been red and swollen for a year. Eye doctor performed a chalazion removal surgery. (Photos)

It looks like you still have eyelid chalazion and blepharitis. See an oculoplastic specialist for further treatment.

You have a lot of lid inflammation still, with some plugged glands.  You would benefit from using low dose antibiotics - doxycycline - which will help to change the secretions from the glands.  The low dose means that it is not actually working as an antibiotic, but as an anti-inflammatory for the glands.  May also need some drops to help with the glands.  See an oculoplastic surgeon who can help with all of this. 

Styes and chalazia occur when the oil glands of the eyelids become inflamed and the glands openings obstruct. Associated conditions include blepharitis, meibomitis, rosacea, other skin conditions, hand-to-eye contact. Initial treatment involves topical antibiotic or antibiotic/steroid ointment, hot compresses to encourage the glands to open and drain, and sometimes an oral medication to control the eyelid inflammation or infection. Some of the underlying factors such as blepharitis are conditions that can not be cured but can be controlled. Your ophthalmologist or an oculoplastics specialist should be able to help you control your eyelid redness and swelling. Best wishes.