Absolutely not. No chance. Herpes doesn't behave anything like you describe.
Both the location and your description are atypical for any STD. Since "at times it seems to have pus in it", most likely it is a pimple, folliculitis, infected cyst, or something along those lines. See a health care provider if it persists or continues to bother you, but don't worry about STDs.
Good luck--- HHH, MD