As a self-employed person, your income would be taxed by the state where the work is performed, not by the location of the company that is paying you for your work.
Since you performed your work in your resident state of SC, the income will only be reported as SC income. No non-resident return for LA will be required.
**Say "Thanks" by clicking the thumb icon in a post
**Mark the post that answers your question by clicking on "Mark as Best Answer"