Small amounts of air commonly enter the stomach with food or water. They gradually come back up in the form of burp/belch/eructation. They increase with intake of aerated drinks. They can be seen in acid reflux
disease or gastritis
Try and sit up the next time you feel air coming up. Lying down or leaning will not facilitate it.
Do visit a physician or a gastro-enterologist for evaluation, since it is causing you distress. It is quite a common problem encountered by physicians, nothing to be embarrassed about.
Hope this helps,
Dr A Rao