There are a couple different possible cause of your pain. First, I would like to clarify where you pain is actually located. The kidneys reside in the mid-lower back. Pain in this area with no trauma can often be caused by a kidney stone.
Kidney stones are small collections of calcium or other material that form within the kidney and can move and get stuck in the ureters. This can cause some severe pain that can radiate from your back down into your groin. Most of the time when someone develops a kidney stone, it occurs on only one side. The sharp pain in your right kidney followed by a lingering pain definitely could be a stone, but it would be unusual to have a dull pain on the opposite side. Pain on both sides could be a sign of a urinary tract infection that has moved up into the kidneys. If you have a
fever, this could be a sign of this.
I recommend that you schedule an appointment with your
primary care physician. He or she can take a more detailed history of your symptoms and perform a thorough physical exam. You will also need to provide a urine sample to look for signs of infection or blood which could be a sign of a urinary tract infection or kidney stone respectively. Good luck.