Yes, you most likely should have received a 1099-NEC instead of the 1099-MISC. The 1099-NEC is for services performed by someone who is not your employee so it seems like it would have been a better option. The NC designation is most likely because you live in NC, but if there was no withholding there is no harm. As long as you report the income on your tax return, there are no issues on your part ( you cannot force them to correct the form, and there may be a reason they did it that way). You can call the IRS to see how to report them if you feel this is appropriate.
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