Keep in mind…
“Pink Eye” is a description of what the eye looks like.
“Conjunctivitis” is a description of one particular symptom (namely, swelling of the conjunctiva (which is the transparent membrane of the eyeball)).
Neither ‘pink eye’ nor ‘conjunctivitis’ describes the full suite of what symptoms there might be. And, most importantly, it doesn’t describe the cause of the illness at all. Not at all.
Pink eye and conjunctivitis can be caused by a viral infection (for which antibiotics are mostly useless), a bacterial infection, allergic reaction, irritation from a foreign substance (smoke, sand, dirty contacts, etc…).
Now, if there’s a huge build up of mucus (‘eye buggers’), then you do likely have an infection.
Peace.