The doc says my herpes culture came back positive? But do I have to take preventive medicine?

No. However if you get frequent outbreaks you may want to consider taking medicines as a preventative strategy.
Need acute treatment. first, Then you can discuss on going preventative treatment to prevent re occurrences and spread to another person with your doctor. The decision to take preventative medication is yours after discussing with your doctor.
Need Treatment Now. You have a positive culture to Herpes Virus and you need treatment with therapeutic doses of Anti Viral Antibiotics.And if this is the first infection following this treatment you do not need preventive therapy unless you keep having recurrence of the Herpetic Lesions. It may be better you discuss all this with your treating doctor as it applies to your case.