It could be a number of things. Do you see any marks that could be from an insect sting or a peck? What does the inside of the eye look like? Are there any bubbles/foam or drainage in the eye? Does the eye look normal? Is there any nasal drainage or sneezing? Respiratory diseases, such as MG or coryza, can cause swelling in one or both eyelids. Coryza stinks, and is much more nasty. MG symptoms may be treated with certain antibiotics as tylosin.
If it is a respiratory disease, pus can form in the sinus cavities and may be able to be expressed by squeezing it out. Tylosin and a few other antibiotics can be used to treat MG. Antibiotic ointment may also be helpful to apply to the eye after cleaning any drainage. This very graphic video shows pus being extracted from an eye: