Don't worry about the barium swallow. That's all it is. You swallow some sweetened barium mixture while they take pictures (x-rays). Not painful, not invasive. It's a good test and will give the answers to whether your esophagus and stomach are working.
Maybe your regular doctor could help you out with something for anxiety, but don't take it before the test. It could affect the results!
PS, after the barium test, and I mean as soon as reasonably possible, drink a lot of anything. Water, tea, coffee. I even take a good dose of Miralax. The barium can clog you and your bathroom plumbing up.