Are the emailed invoices suppose to show up in your actual email account in the sent box?

These invoices will only show once you email yourself a copy or you CC or BCC yourself, Reneeiley.

Let's check your settings to verify you've turned on these options. Here's how:

1. Click the Gear icon.
2. Select Account and Settings.
3. Go to the Sales tab.
4. Click the Pencil icon in the Messages row.
5. Check if the Email me a copy box is ticked, and there are email address in the Copy (CC) and Blind Copy (BCC) fields. 

I'll include screenshots for better guidance. 

If you wish not to receive any email, you can uncheck the box, then delete the email addresses.

Let me share an article about emailing and printing an invoice for future reference. 

I'm here if you have more questions. You can tag me and I'll answer you as soon as I can.