Sending serial commands to yourself
Yes, you can do that by cross-connecting the transmit and receive pins on the Arduino. But then your devices sits there silently murmuring to itself (or not...) and you can't really tell what it's saying, or if it's doing anything unless you can observe some other hardware - LEDs, a 'scope, f/ex.

But why not hand-type or script some messages to it on your PC? If the Arduino sketch would make some brief, coherent replies you could confirm what it's doing and debug it if necessary.

I've done just this in your situation: Two of us defined a serial protocol - the ASCII (for human readability!) commands and replies that either end could make or expect. Then each of us wrote the communication code for one of the two devices and proved that it met the protocol. Once both of us had finished and were confident in our respected communication code, we plugged the two devices together, and - they played! Nicely! :)  And if they hadn't we could have eavesdropped on the serial line and printed their attempted conversation to discover where it went wrong.