A 35-year-old male presents to an outpatient clinic with a chief complaint of progressively worsening eye discomfort over the past three days. He reports that his eyes feel "gritty" and "sandy," especially upon blinking. Each morning, he finds his eyelids stuck together by a thick, yellowish, and sometimes greenish discharge, which he describes as "pus-like." He frequently needs to wipe away this material from his eyes throughout the day. His vision remains generally clear, though occasionally blurred by the discharge, and he denies any significant eye pain or severe light sensitivity. On examination, both conjunctivae are diffusely hyperemic with a prominent "bloodshot" appearance. There is moderate purulent discharge present, particularly in the inferior fornix. The eyelids show mild edema and crusting along the lash lines. Pupillary reactions are brisk and equal, and intraocular pressures are within normal limits. Visual acuity is 20/25 in both eyes, improving to 20/20 after discharge removal. Based on these findings, what is the most probable diagnosis and the recommended initial management strategy?