If TurboTax notified you that your return was accepted by South Carolina, it should not need to be submitted again. I am attaching a link to an FAQ for South Carolina's refund site. On the site it does say it is normal for it to say the refund is not processing for a few weeks. There is a phone number to contact if you have any issues or need more assistance.
https://dor.sc.gov/tax-index/individual-income/Pages/refund-status-progress.aspx
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