For this year the parents are not filing a Schedule H as they appear to be treating you as self-employed. They should issue you a form 1099-NEC, but you are responsible for reporting your income whether or not they issue a 1099.
You will enter your childcare income and expenses in the "Self-employment" topic under the "Income & Expenses" tab.
The licensing question is not a tax issue, but a state/local legal issue so we can't respond to that question in this forum.
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