For years I had a mass on the bottom left abdomen, very similar to yours, pulsing and all. There were times when I had severe constipation and that area actually started to burn and I could feel the mass, touch it, and be in a lot of pain.
I started linking my other digestive issues to the possibility that something was there, a blockage, some kind of cyst I don't know. However it did not really "manifest" in that area, rather id get a digestive issue and be like hmm maybe its that mass in the abdominal causing it.
I got a colonscopy, all good. Then they did a ct scan and found that my kidney is actually in the wrong place, it is in the front rather than the back and that was what iwas feeling.
The reason I had the burning that time was I had a bit of a blockage and it rubbed against the kidney. Also im sure there can be other weird effects when you have digestive issues with a kidney in such close proximity.
I'm not sure about the X-rayu they did on you,but you should get a real CT scan of that area.That was an eye opener for me, because I always assumed the mass was a blockage/cyst/etc.