You don't need to enter information from your Form 5498 (IRA Contribution Information) into TurboTax. You should keep Form 5498 with your records for future reference when you need to determine the end of year value or your investment basis in non-deductible or Roth IRAs.
As long as you didn't have a distribution from your IRA or have a "rollover" to another retirement plan, you will not receive a 1099-R.