Niki. The same pathophysiologic process that causes heartburn also causes you to burp. That is, your lower esophogeal sphincter tends to be weak, leading to heartburn (i.e. acid from the stomach irritates the lower esophagus). The same weakness in the sphincter may also cause air in your stomach to escape, resulting in burping. Add to that the irritation from the stomach acid on your esophagus, and your stomach/esophagus may spasm, leading to burping.
In terms of stopping the heartburn, you have many options. One, you can try to avoid food triggers that cause heartburn for you and avoid eating right before bed. Two, antacids like Tums or Mylanta will help. Three, drugs known as H2 blockers that are sold over the counter will help, including Tagamet, Pepcid or Zantac. Finally, drugs to reduce acid secretion known as proton pump inhibitors also exist. Most require a script, but Prilosec OTC is sold over the counter.
I would suggest reducing your food trigger intake and starting with some antacids. If that doesn’t work, try the H2 blockers or Prilosec OTC. If you are also having stomach discomfort or your weight has been changing, you should go see your doctor since you might have an ulcer.