Swollen skin around the eye, yellow discharge but white of the eye is clear and not bloodshot - conjunctivitis?

[ButtfaceMiscreant]

As the title says, DD (12mo) woke up with a swollen eye (skin only) and yellow discharge. Her eyeball is not red at all. Been to the GP who didn't look at her eye really, just prescribed chloramphenicol (sp?) eye ointment. I just was wondering whether it is actually conjunctivitis without a bloodshot eye?

For what it is worth, I will treat her with the ointment as per GP instructions, I was just wondering if she does have conjunctivitis based on her symptoms, as Google only suggests she would have bloodshot eyes with it.

She had a blocked tear duct for the first 6 months of her life with continual gunk and occasional redness, and it looks very similar to that.

Thanks in advance!

My lo has conjunctivitis at the moment. It was red last week but now just has crusty discharge and faintly swollen. (She still has a cold which is why it's hanging about) the eye itself is white, doesn't seem to bother her.