That's correct. When you work but are not paid as an employee with a W-2, you are considered to be self-employed. Your income and any expenses you might have are entered on Schedule C, Profit or Loss from Business. Since the person for whom you work did not withhold taxes, you are responsible for them.
From
<https://www.irs.gov/faqs/interest-dividends-other-types-of-income/1099-misc-independent-contractors-and-self-employed/1099-misc-independent-contractors-and-self-employed-1>