No. You should not be alarmed. You didn't say whether you e-filed or filed by mail. If you e-filed and TurboTax said your return was accepted, the IRS has it.
If you filed by mail, there’s probably a larger chance your state refund would come first because the IRS is backed up processing paper returns.
Keep checking Where’s My Refund? IRS says call only if Where's My Refund? directs you to contact them.
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