The CBC test stands for complete blood count; it measures the numbers and types of white blood cells, and the numbers of red blood cells. It also measures hemoglobin (the molecule that transports oxygen on the RBC) and the hematocrit; the percentage of red blood cells in the sample. It will also show how big and wide those red blood cells are.
White blood cell counts do change in response to illness. In fact, the different types of white blood cells each specialize in fighting different things. So a rise in one category of WBC can help indicate what the culprit MAY be.
However, it is not an STD test. It wont show that there is an STD, it will only show an elevation in the numbers of white blood cells. And not all STDs will create such rises, either.
Urinalysis also wont indicate an STD as conventional ones don't check for one. They will show if there are blood cells in the urine, protiens, and ketones (what happens when tissues are broken down), and tell if the urine is too concentrated or too dilute. Urine cultures will check for a urinary tract infection by seeing what germ grows...but that is not an STD test, either.
The best way to know if there is a STD is to test for them. Here is more information on STDs: http://www.fwhc.org/health/std.htm
I hope I was able to clarify for you,