am i considered as self employed?

Yes, if the family pays you directly for the care you provide then you are now officially self-employed! As a self-employed individual you will report your income as business income and you can also deduct certain expenses that you have related to the work you do. 

As a caregiver to a private family you might have expenses such as:

• mileage that you drive to perform your work or run errands for your employer
• uniforms
• protective equipment (masks, gloves, etc.)
• supplies and equipment necessary for your work
• licensing fees
• education 
• gifts for the family

This isn't an exhaustive list, but just meant to get you thinking about some of the things that you might want to make note of to gather before you sit down to work your taxes this year.  These expenses will help to lower the amount of tax that you will pay on your income since you're taking on the responsibility of not just your income tax but now the self-employment tax as well which is the social security and medicare portion that most employees share with their employer when they work in traditional settings.  

We have a more extensive overview of filing as self-employed here: Reporting Self-Employment Business Income and Expenses.