My son had a scattered amount of little white "pimples" all around his left eye when he was 2 1/2... Molluscum, something? First it was a couple, then it was like 15! They didn't go away, so I took him to the doctor. They were from a "virus" and the doctor said I needed to just "pop them" and they would go away! DO NOT DO THAT until you take her to get them checked first of course.
I asked him to demonstrate, and literally, he dug his nails in a squeezed one out. It bled and really hurt. Little by little, over the span of about a week, I popped a few per day-just had my husband help hold him while I dug in a squeezed and he screamed, and then he got some treat like chocolate. Finally, all he had left were red scabs, and those went away and they were all gone! So it may be that. Take her in to be checked!
Stys are in the ducts of the lids, that doesn't sound like what you're talking about.