How do i know if an invoice i generated and sent was actually sent and received?

It's great having you here in the QuickBooks Community, dhouston. 

I'm here to help resolve your concern about knowing if the invoices you've sent have been received by your customer using QuickBooks Self-Employed (QBSE). 

The sent invoices don't appear on your Outlook window because QBSE uses Intuit's email service address, quickbooks@notification.intuit.com, as the sender instead of your Outlook email.

Since there's no direct way to check if an invoice has been received on your customer's end, it's best to coordinate with your customer if the invoice has been received. If the invoice hasn't been received, you can choose to resend the invoice. Moving forward, ensure to put a checkmark on the Send myself a copy box to confirm if the invoice has been successfully sent to the customer.

As a future guide, let me add this article if you need a reference to add sales taxes for your products and services in QBSE: Manually track sales tax in QuickBooks Self-Employed.

Keep us posted if your customers weren't able to receive the invoice emails you sent through QBSE. We'll do our best to assist. Take care.