Despite the fact that you say "I am not self-employed nor I own a business", s far as the IRS is concerned that is what your are, unless you want to get your "employer" in trouble for not treating you as an employee and remitting payroll taxes.
The IRS considers undocumented cash income (no W-2 or 1099-MISC), for work performed, to be self employment income. Enter at "Business Income & Expenses" and TurboTax (TT) will complete Schedule C or C-EZ for you and allow you to deduct any expenses associated with this income. You'll also have to pay self employment tax (social security & medicare tax) on any profits greater than $400. You report the income from your own records.
