Yes, you should file a Schedule C for the 1099-NEC income.
The type of income is non employee compensation, it is business income. It is therefore subject to self-employment tax and the self-employment tax is calculated from the net profit (1099-NEC minus expenses), as well as the deduction for one half of self-employment tax.
For more information on how to enter the 1099-NEC follow this link: How do I report income from self-employment? Please note the form referenced in this link is 1099-MISC but that has changed to form 1099-NEC.