Why would anyone X-Ray soft tissue??! That's a serious question for your doctor. Look, MD's are a necessary evil sometimes. Lay people can't just walk into a facility and request diagnostic tests. We must rely on doctors to "prescribe" such tests. We also rely on their expertise to know when such tests are needed and exactly which tests should be performed. This is why we use Westen Medicine ---- diagnostic tools not available to the general public and trauma, such as a broken leg or deep gashes that require stitches. Right now, you still need them, but you need to find one who knows what the heck he's doing. Or actually gives a shit about his patients.
Sorry to sound harsh, but your doc dropped the ball on this one.
With all that said, there's a very strong chance it's just your abdominal aorta that you are feeling and it is no big deal. I wish I knew what makes it pulse stronger at times and what causes the lump, but I don't. My uneducated mind always goes back to those nifty diagnostic tools to rule out the obvious: abdominal aortic aneurism. Good luck!