No, just state babysitter, city and state and dates. Of course, you should be aware that not all immigrants can legally work in the US, and I think you should be filing the forms with the help of an attorney. Good luck!
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You may have been an independent contractor and not an employee, so you can indicate self employed and the job title.
The above is intended only as general information, and does not constitute legal advice. You must speak with an attorney to discuss your individual case.
You can answer babysitter and state local families as your employer, but more importantly it sounds as though you may also need to be prepared for the affidavit of support for the immigrant visa petition.