You do not need to have Form 1099-MISC in-hand to report the income.
You will not have any problems with your return, as long as the income you report on your Schedule C equals or exceeds the total amount reported on any 1099s that are filed reporting your income.
When you enter the information in TurboTax, just select Additional Income (see screenshot below) to report income for which you have not received a 1099.