My daughter had one on her lower lid when she was 2 or 3 and it took many months to go away. She also developed one on her upper lid which is not red, but has never fully gone away at 51/2. (they can stay forever unless removed.) I'm sure you don't want to hear this, but she needs to go to an eye doctor. Pediatric if you can, but call around and look into who will see her. When we took our daughter to the regular pediatrician they put her on antibiotics, which we learned later were worthless in this case. If you can start the proper drops within a week of it showing up, then they often help. Otherwise, they are usually useless-according to our pediatric ophthalmologist. If it is a stye, it may go away easier but requires the same home treatment. A chalazion is actually a clogged tear duct or oil gland. It may have something to do with makeup, but very well may not.
What you can do right now is warm compresses. Heat up a mug of water-not too hot. You can add salt as well. Use makeup cotton squares or rounds, again on Dr.'s advise, they work the best. Just get one wet with very warm water and hold it on the eye. Change out for fresh warm compress for five to ten minutes. I know that sounds like a lot, but let her watch TV(with the other eye) while you do it. Also, you can use a clean cloth or the pads and wash her eyelid with baby shampoo each night. A tip form another ophthalmologist.
I hope this helps. Good luck.