It sounds like its possibly a hiatal hernia. A hiatal hernia is a condition in which a portion of the stomach protrudes upward into the chest through an opening in the diaphragm (the sheet of muscle used in breathing that separates the chest from the abdomen).
Some hernia's can be pushed back into place with your hand. This is much more common when the hernia is in your abdomen or groin. You may have found a position in which this stretching your doing is pushing your stomach back to where it's supposed to be with a distinctive "pop" feeling.
An untreated hernia will not get better on its own, although it may not get worse for months or even years.
The only cure is surgery. There are two reasons for hernia surgery: to correct or prevent a dangerous strangulated hernia, and to eliminate the pain that may be interfering with your normal activity.
I would definately seek the advise of a gastroenterologist. If it ever gets to a point where you can't get it to stop (go back into place), it will get worse and worse and become a serious medical condition as stangulation of the sqeezed portion results in gangarene. So don't mess around with this. Good luck