You would be reporting self-employment income and expenses. You enter your income and expenses on Schedule C. You can enter the income you received without a tax form from your client (you were not an employee).
You will need to upgrade your TurboTax online account to the Premium online edition which support Schedule C.
See this TurboTax support FAQ for Schedule C - https://ttlc.intuit.com/turbotax-support/en-us/help-article/import-export-data-files/enter-schedule-...
