STDs are localized infections, and don't always cause an increase in WBC on a CBC. SED rate has to do with inflammation, and has nothing to do with STDs.
Aj
Normally a CBC will not give a determination either way.
I understand that in order to find out what specific infection you might have you need a particular test but if you had an infection would your white blood cell count be up and if so wouldn't it be found on the cbc test as just an indication that you have an infection not what type of infection.
STD's have specific tests, a routine bllod test would not have anything to do with an STD test.