Yes, if you earned more than $400 in cash, the IRS considers you to be self-employed and you are required to file a Schedule C, business income and expenses and pay self-employment tax (Social Security and Medicare-same as withholding on a W-2).
If you don't get a W2 and they don't take taxes out of your pay that is self employment income.
You can enter Self Employment Income into Online Deluxe or Premier but if you have any expenses you will have to upgrade to the Self Employed version.
How to enter income from Self Employment
That's $400 net for the year.
When you report self-employment income is $400 or more, after deducting expenses, Schedule SE will generate in TurboTax.
Please see the TurboTax Help articles Why am I paying self-employment tax? and Does a 1099-NEC or 1099-MISC mean I'm self-employed? for more information.