That's a new one on me, "...you're young, and don't need an endoscopy." Aside from seeing the function of the swallowing muscles, and the integrity of the LES, a barium swallow doesn't offer much more information. The only way you can diagnose GERD is through either a 24-hour pH impedence, or a 48-hour Bravo pH study. The impedence test is becoming more and more difficult to find, as it has been replaced by the Bravo. The impedence has the advantage that it can be administered without anesthesia, records acid as well as non-acid reflux, and also will record how high it travels -- even into your throat. The Bravo offers more complete data on individual reflux episodes, time-of-day, etc., but has the disadvantage that it must be implanted during an endoscopy.
An endoscopy would also allow your doctor the means to visually inspect your throat, to see if there are erosions, etc., but an ENT could also scope your throat in his office without anesthesia.
A barium swallow is only one test of several that could be important. For your doctor to suggest that that's all is necessary, sends up a red flag in my experience. He may very well be a good doctor, but I'd be ready to find a second opinion.