No, it sounds like you are handling it properly. While the job may have been at the same employer location, it was not the employed position, but instead treated as an independent contractor. There was no Social Security, Medicare or income tax withheld.
The self-employment tax is the employee and employer portion of Social Security and Medicare. Just as the employer would, you receive a deduction for the employer half of these expenses.
The self-employment tax is 15.3% and the income would also be subject to income tax. The amount subject to these taxes is the net profit after expenses.
