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Is it painful and tender? Is the white stuff looks cheesy or oily? Has it some smell?
A few more clarifications, would be helpful:
The ring (redness) around it is still there and a little darker.
Thank you for the input.
Your daughter seems to have had either an Insect Bite reaction with local abscess formation or a secondary infected sebaceous cyst( that would account for the white stuff coming out). The red ring is an inflammatory ring. As you have already lanced it and the content has been drained, hot water soaks is all that is needed now for a couple more days.
If the red ring is spreading and still the discharge is coming out, she should be taken to her pediatrician or GP for prescription antibiotic and full drainage.