Parents are not allowed to claim a child's wages on their tax return. I hope that he "includes" your amount to the household income for healthcare reasons and subsidy purposes but NOT to claim your wages as his income on his tax return... you may want to verify that.
Having said that, since you are paid through a W-2, your wages are subject to a "regular" income tax rate (on your tax return, if you are required to file); you don't own a business and self-employment tax rate does not apply to you.
Your wages are completely separate and unrelated to your father business taxes.
If you are claimed as a dependent on your dad's tax return, please read Do I need to file my own taxes if I'm a dependent? If you are not, please follow Do I need to file a federal return this year? If you are not required to file, but your W-2 has federal and/or state withholdings, you may want to file to get that withholding back.