Yes, to the question about entering them in Estimated Payments.
No, to the question about Schedule H. As stated before, Schedule H is for paying those same taxes that you have already paid as a tax on your Form 1040.
In order to indicate the taxes you have paid already during the year for your household employee (or others), you need to:
1. Go to "Deductions + Credits" (on the top bar)
2. Select "Estimates and Other Taxes Paid"
3. Select "Estimates"
4. Under "Estimated Tax Payments", select the first option "Federal estimated taxes for 2019 (Form 1040ES)"
And there you can enter the payments you have made during the year (each quarter).
