Let me help and provide information about entering EIN in QuickBooks Self-Employed (QBSE).
Currently, the option to enter your EIN number in your tax profile isn't possible in QBSE since this is designed for Independent Contractors. You can only enter your EIN in QuickBooks Online.
For QBSE, to pay for your quarterly tax, you can either pay by mail or online. Here's how to pay by mail:
In QBSE, go to the Taxes menu.
Select the Quarterly Taxes tab.
Select Pay Now.
Select the By mail option.
Fill out the 1040-ES payment voucher. Then, select Continue
Print your voucher.
To pay online, you'll have to sign up for an Electronic Tax Payment System account: