You may end up seeing both! The tests that the urologist will run will probably determine the need for a kidney specialist.
The urologist will most likely deal with the kidney stone & perhaps the blood in the urine, a kidney specialist will most likely deal with the protein in urine. But, the first step is generally the urologist! If you are not satisfied with the way this is being handled, you can ask to see a specialist first. I would imagine that they would run the same tests.
I wish you the very best
Peace and Blessings
Look For The Good and Praise It!