I had something that sounds like this and it would sometimes last for days or even a week or so.  What it turned out to be was the blood vessels in the groin and around the testes, more or less, constricting and irritating everything they surround due to heavy lifting.  I had lived with this on and off for many years and doctors couldn't figure out what it was.  One day I went to a urologist for something unrelated and I thought I'd mention this problem.  He said it was probably the blood vessels in the groin and other doctors probably didn't make the connection because this typically is seen in older men who have spent a lifetime doing heavy work.  I had surgery to remove the blood vessels a couple of years ago and occasionally I only suffer very mild symptoms after doing hard work and lifting.

My boyfriend who is 26 years old is experiencing the same thing. He gets this lower right quadrent pain that comes and goes as well as testicular pain. He does not take any medication and works out everyday. He is very in shape however this pain sometimes gets in the way of his daily routine. It seems to be worse in the morning and get better as the day goes on but sometimes it is unbareable. He also started to get this shooting pain up the right side to about his belly button from the lower right quadrant. He has the same concerns as you. Please let us know if you hear anything as this would be greatly appreciated.