Hi, loustar.
I don't know the anatomical cause, but I can say that I had various levels of pain in my abdomen for a couple of months, post-donation. Usually, it took the form of constriction-type pain.
One thing that definitely caused pain, for many, many months, was a bumpy bus ride.
Also, of course, there are restrictions about how much you can lift after surgery; lifting was another issue that took quite a while to resolve for me. Even for quite a while after it was "legal" for me to lift, it usually caused some pain.
Fortunately, though, the pain was never severe. More often, it was closer to discomfort than real pain. I hope your pain goes away soon!
Be well, Snoopy