Call the IRS's toll-free number at 800-908-9946 to ask if the payment has been credited to your tax account. Tell them you made a payment. Have your credit card statement ready with the date and transaction number. Confirm payment to the IRS with your credit card provider in advance.
If your credit card statement shows the amount was paid then who was the payee? The credit card statement is your proof of payment.
Look at your tax account on the IRS website to see if you still have balance - https://www.irs.gov/payments/view-your-tax-account
if you have a credit card statement showing the charge made to the IRS, then that's all the proof you need. TurboTax is not involved in the payment. We simply send the information on how you want to pay your tax to the IRS and only they can initiate the transaction. If the charge hows on your statement then the IRS made the charge and knows about the payment.
Is the amount on your credit card statement the same amount the IRS says you owe? Maybe the credit card charge is just for the Turbo Tax fees? What is the description on the charge?