Be patient. Like you said the date on TurboTax was just an estimate. It is based on the fact that most refunds are issued within 21 days of the return being accepted, it is not an official date that was ever provided by the IRS who has complete control over your Tax Return and Refund.
Processing simply means that the IRS is working on your return, it is the stage after accepted and before being approved. Here is more information on what's happening with your return
https://ttlc.intuit.com/replies/4689484
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