Impossible to tell from a picture like that. Need to see the whole eye, and the other for comparison.
Conjunctivitis usually comes with red, sticky eyes, that feel very tired and gritty/irritated. Were your eyelids stuck together when you woke up this morning?
But if they don't currently feel sore, itchy or red, the pharmacist won't give you the drops for them. What actually are your symptoms? That tear on your eyelashes?