It is possible that the IRS adjusts your return and sends you an additional refund, but that will most likely take a year or more. It takes the IRS quite some time to match income records to your Tax Return and make adjustments.
I highly recommend that you go ahead and Amend your Tax Return after the IRS fully processes your return and you receive your refund.
Then, you should Amend your Tax Return by filing Form 1040-X to include the correct Form 1099-R information.
You can click here for instructions on Amending your tax return: How to Change a Tax Return You Already Filed. TurboTax will walk you through Amending your State Tax as well.
