I am paid by the total time I see patients.

Payment is rendered after the service is provided generally.

The question I have is: Can I create an invoice where the payment is shown and an amount owed (if needed) is also shown.

Essentially, this is a receipt.

Thanks.

What you could do is print a statement (new in Billings 3) which would show any invoices and payments for the client, giving the total amount owed (if any). This is not really part of an invoice as you have suggested, but does give the client a record of their payments.