Welcome to the Pain Management Forum. I am glad you found us and took the time to post...but sorry to hear about your bulging painful area.
Do you have any gastrointestinal problems associated with this "lump?" It's possible it could be a hernia....it's the reduction that leads one to believe that may be the case.
Your breast bone is medically known as the sternum. Your xiphoid process is located in that area but it shouldn't be reducible. The sternum is shaped like a sword. It is elongated and flat and extends from the base of the neck to the pit of the abdomen. At the very bottom portion of the sternum is a cartilage called the xiphisternum or xiphoid process, Sometimes is can become harden and curl upward. However this should not be reducible.
In that area the hernia that is most prevalent is a Hiatal Hernia. I have one...and 60% of America develop one before the age of 60. I have never heard of this being palpable or reducable. That doesn't mean it never is....
Here's a link to one discussion on MH regarding similar symptoms:
It's always best to consult your PCP. Your symptoms have been going on for five years...it's time to obtain some answers. It's probably nothing serious but having a physician tell you this will ease your mind.
Please let us know how you are doing. We will look forward to your updates and wish you the very best.