My 3 year old daughter had a sty on her eye lid and it popped about a week ago. Now the whole eye is swollen red/purple looking and it's spreading.
Cellulitis. For now I would continue to do warm compresses if she will sit still long enough to allow you to and I would have her seen ASAP because what you describes sounds like a deeper infection like cellulitis that has to be treated with antibiotics eye drops and oral. I hope this helps. Please let me know what the local doctor says.
See peds. It sounds like the infection has spread and could be a periorbital cellulitis. This would likely require oral antibiotics for treatment. Don't delay, call the pediatrician today (there's always somebody on-call) and they will be able to direct you. Warm compresses can be helpful before and during the oral antibiotics and can be soothing for your child.