I recently heard a burping sound in my right ear. what could be going on?

Eustachian tube: Your Eustachian tube drains the middle ear fluid into the back of your throat. Sometimes there are pressure changes and you can get a sound like that from the Eustachian tube opening up if it has been blocked temporarily. It is nothing to be concerned about.

Normal: This was likely due to movement of the tympanic membrane (ear drum) associated with changes in pressure in the middle ear. It is usually occurs with swallowing or changes in atmospheric pressure, including ride in an elevator.