Just a thought. Do you do other PE such as jelks, squeezes, bends, uli’s? If you use your right hand to make an “OK” turniquet grip at the base you may inadvertantaly bruise the underlying tissue with your thumb or finger tip. The palm side of the hand will spread the load evenly but the finger side can create very high pressure in a small area. Again, I am just speculating but your hanging could be revealing an injury substained from the above process.
Another concept I think Bib has commented on is that your body may have slightly different structure from side to side. Even if your penis does not bend it may still have different ligament strenght side to side. If your right side is stronger, the left side may be incurring more micro tears and therefore be sore. At some point this should equalize.