Is it true that if you need to flatulate and hold it in, it will come out as a burp?

Yes, it is true that holding in flatulence can result in a burp. This happens because they both originate from the same source — your stomach.
When you hold in flatulence, the air pressure builds up and needs to escape somewhere. The only place for it to go is back up your esophagus and out of your mouth as a burp. That's why people often burp when they hold in gas—it's an effective way of releasing the built-up air pressure.
So while technically you're releasing the same gas through a burping episode as you would have with a fart, it typically contains different levels of nitrogen, hydrogen sulfide, carbon dioxide and methane. These differences are what make farts smell so much worse than regular belches!