First line:

Eyelid hygiene is the mainstay of treatment for both blepharitis and hordeola. Advise application of a compress with warm (not scalding) water to the eye area for 5-10 minutes, four times a day during acute infections or flare-ups. 

Second line:

If hygiene measures for two weeks have not resulted in resolution of symptoms, a 6 week trial of chloramphenicol 1% eye ointment applied twice daily

A stye or hordeolum is an acute infection of the tarsal oil glands of the eyelid and presents as an abruptly developing tender swelling on the eyelid. Blepharitis is a chronic inflammation of the eyelids. Patients with blepharitis will most commonly complain of chronic irritation of the eye, often accompanied by redness. There may be intermittent exacerbations of symptoms. Hordeola can be associated with blepharitis due to abnormal oil secretion.

If symptoms are persistent or severe, send a swab of the lid margin.