It could be pink eye. They sell antibiotic eye drops over the counter (called Polysporin here in Canada) that work wonders. Or you could check with your doctor, just to be sure that this is really what is causing the symptoms you've described. If it is pink eye, it's highly contagious and she should be kept away from other children as much as possible until the symptoms have subsided.
I don't know how old your daughter is, but I've used the drops on my youngest sons's eyes when he was a newborn - upon the advice of my GP. As always, you should consult your physician if you're unsure.
I agree with Limonada. Until you contact your daughter's pediatrician and make sure he's OK with the drops, you can go to the store and buy sterile saline drops (salt water). they sting a little but if you put a few drops in the affected eye it helps start the healing process. my daughter (who was about 14 months at the time) and I both had a REALLY bad case of pinkeye and we used saline drops overnight and the next day the pinkeye was completely gone. I've had pinkeye several times (many times in high school because I was on the swim team) and it always took like a week to clear up...but the saline cleared it right up and it's safe...salt is a natural antibacterial/antibiotic.
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