You can have kidney problems without having some sort of major kidney desease--trust me. It's like lazy eye but in your kidneys--if you feel it in both sides of your back--it's probably the ketosis stressing them out--drink more water or anything not caffinated--try to lower salt intake too.
It is very hard for your kidneys to filter and dispose of ketones--if you don't drink enough you are making it even harder. Plus--I know everybody thinks they want their ketostix to be in the high range but you really don't. If you get into high start drinking like a mad man until your stix read moderate. If you don't you will cause the ketones to back up in your system and they become poisonous to your body (starts turning into acetate I think). Plus the more ketones floating around in your system, the less your body will produce--trying to save itself--if you flush them out with liquids your body will feel it is still in a safe range and not slow down the process.
If the back pains turn severe--you will know this by now--and are on one side of your back mostly, you have kidney stones. They take the worlds most tiniest path from your kidneys to your bladder--it will tear you up (they are very jagged), be overwhelmingly painful and turn your pee slightly reddish (from blood).
So if your not in the hospital begging the doctor for morphine right now and increasing fluids/decreasing sodium doesn't help, I would suggest seeing your family doctor and just having him do a simple urinalysis (about $20)--can check for simple bacteria infection, microscopic bleeding (you can't see), protiens/sugars and other signs of malfunction.